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Zhang X, Zhao Q. A Kundu-nonlinear Schrödinger equation: Rogue waves, breathers, and mixed interaction solutions. CHAOS (WOODBURY, N.Y.) 2024; 34:053135. [PMID: 38787312 DOI: 10.1063/5.0186265] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2023] [Accepted: 05/06/2024] [Indexed: 05/25/2024]
Abstract
A Kundu-nonlinear Schrödinger equation that can be utilized to simulate the pulse propagation in optical fibers is researched in this paper. First, the Lax integrability of the above equation is proved and its modulational instability (i.e., the main mechanism for producing the rogue wave solutions and the breather solutions) is calculated. Subsequently, using the generalized perturbation (n,N-n)-fold Darboux transformation, the rogue waves, breathers, and mixed interaction solutions are acquired, as well as the impact of various parameters on the solutions is examined. In particular, when we assume that the coefficient of the equation is θ=mx+dt, some new wave structures are found based on parameter variations, such as the rotational separation of first-order rogue waves, scale-like structures generated by second-order breathers, etc., which offer novel ideas for producing different signals via optical fibers. Ultimately, the classification numbers of mixed solutions of rogue waves and breathers are provided, which can better observe how the two types of the local waves are combined, in accordance with the distributions of the increasing numbers of algebraic equations.
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Affiliation(s)
- Xuejie Zhang
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, People's Republic of China
| | - Qiulan Zhao
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, People's Republic of China
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2
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Knobloch E, Yochelis A. Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics. CHAOS (WOODBURY, N.Y.) 2024; 34:051103. [PMID: 38787315 DOI: 10.1063/5.0205658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 05/06/2024] [Indexed: 05/25/2024]
Abstract
Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensates. We describe the emergence of rogue wave-like dynamics in a reaction-diffusion system that arise as a result of a subcritical Turing instability. This state is present in a regime where all time-independent states are unstable and consists of intermittent excitation of spatially localized spikes, followed by collapse to an unstable state and subsequent regrowth. We characterize the spatiotemporal organization of spikes and show that in sufficiently large domains the dynamics are consistent with a memoryless process.
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Affiliation(s)
- Edgar Knobloch
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Arik Yochelis
- Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
- Department of Physics, Ben-Gurion University of the Negev, Be'er Sheva 8410501, Israel
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3
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Geng J, Fu L, Dong H, Ren Y. Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves. CHAOS (WOODBURY, N.Y.) 2023; 33:123135. [PMID: 38154040 DOI: 10.1063/5.0176812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2023] [Accepted: 11/28/2023] [Indexed: 12/30/2023]
Abstract
The Cartesian coordinate system is not sufficient to study wave propagation on the coastline or in the sea where the terrain is extremely complicated, so it is necessary to study it in an unconventional coordinate system, fractals. In this paper, from the governing equations of fluid, the fractional nonlinear Schrödinger equation is derived to describe the evolution of Rossby waves in fractal by using multi-scale analysis and perturbation method. Based on the equation, the rogue-wave solution is obtained by the integral preserving transformation to explain some serious threats at sea.
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Affiliation(s)
- Jingxuan Geng
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
| | - Lei Fu
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
| | - Huanhe Dong
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
| | - Yanwei Ren
- College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China
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4
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Chowdury A, Chang W, Battiato M. From rogue wave solution to solitons. Phys Rev E 2023; 107:014212. [PMID: 36797948 DOI: 10.1103/physreve.107.014212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2022] [Accepted: 01/08/2023] [Indexed: 06/18/2023]
Abstract
Using a generalized nonlinear Schrödinger equation, we investigate the transformation of a fundamental rogue wave solution to a collection of solitons. Taking the third-order dispersion, self-steepening, and Raman-induced self-frequency shift as the generalizing effects, we systematically observe how a fundamental rogue wave has an impact on its surrounding continuous wave background and reshapes its own characteristics while a group of solitons are created. Applying a local inverse scattering technique based on the periodization of an isolated structure, we show that the third-order dispersion and Raman-induced self-frequency shift generates a group of solitons in the neighborhood where the rogue wave solution emerges. Using a volume interpretation, we show that the self-steepening effect stretches the rogue wave solution by reducing its volume. Also, we find that with the Raman-induced self-frequency shift, a decelerating rogue wave generates a red-shifted Raman radiation while the rogue wave itself turns into a slow-moving soliton. We show that when third-order dispersion, self-steepening, and Raman-induced self-frequency shift act together on the rogue wave solution, each of these effects favor the rogue wave to generate a group of solitons near where it first emerges while the rogue wave itself also becomes one of these solitons.
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Affiliation(s)
- Amdad Chowdury
- School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore
| | - Wonkeun Chang
- School of Electrical and Electronic Engineering, Nanyang Technological University, 639798 Singapore
| | - Marco Battiato
- School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore
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5
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Bai XD, Zhang D. Search for rogue waves in Bose-Einstein condensates via a theory-guided neural network. Phys Rev E 2022; 106:025305. [PMID: 36110015 DOI: 10.1103/physreve.106.025305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Accepted: 07/25/2022] [Indexed: 06/15/2023]
Abstract
An important and incompletely answered question is whether machine learning methods can be used to discover the excitation of rogue waves (RWs) in nonlinear systems, especially their dynamic properties and phase transitions. In this work, a theory-guided neural network (TgNN) is constructed to explore the RWs of one-dimensional Bose-Einstein condensates. We find that such method is superior to the ordinary deep neural network due to theory guidance of underlying problems. The former can directly give any excited location, timing, and structure of RWs using only a small amount of dynamic evolution data as the training data, without the tedious step-by-step iterative calculation process. In addition, based on the TgNN approach, a phase transition boundary is also discovered, which clearly distinguishes the first-order RW phase from the non-RW phase. The results not only greatly reduce computational time for exploring RWs, but also provide a promising technique for discovering phase transitions in parameterized nonlinear systems.
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Affiliation(s)
- Xiao-Dong Bai
- Department of Mathematics and Theories, Peng Cheng Laboratory, Shenzhen 518055, Guangdong, People's Republic of China
| | - Dongxiao Zhang
- National Center for Applied Mathematics Shenzhen (NCAMS), Southern University of Science and Technology, Shenzhen 518055, Guangdong, People's Republic of China
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6
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Tan Y, Bai XD, Li T. Super rogue waves: Collision of rogue waves in Bose-Einstein condensate. Phys Rev E 2022; 106:014208. [PMID: 35974525 DOI: 10.1103/physreve.106.014208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 06/17/2022] [Indexed: 06/15/2023]
Abstract
An important and incompletely answered question is whether a high-order rogue wave (RW) can be excited by the collision of first-order RWs, especially for its generation and propagation mechanisms. In this paper, the evolution properties of collisions between RWs are studied numerically for two-component coupled Bose-Einstein condensates. We find that whether a second-order RW can be successfully excited strongly depends on the location and time of the first-order RWs encountered. Only when the highest peaks of two RWs meet at the same position at the same time, can the standard second-order RW be triggered and its structure is in good agreement with the exact solution. Further, we demonstrate that such results are also applicable to the collision of subordinate RWs. This paper not only reveals the collision properties of RWs, but also provides a feasible scheme to generate higher-order RWs for experimental realization.
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Affiliation(s)
- Yanchang Tan
- Department of Physics, Xiangtan University, Xiangtan 411100, China
| | - Xiao-Dong Bai
- Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518005, China
| | - Tiantian Li
- Department of Physics, Xiangtan University, Xiangtan 411100, China
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7
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Bright, Dark, and Rogue Wave Soliton Solutions of the Quadratic Nonlinear Klein–Gordon Equation. Symmetry (Basel) 2022. [DOI: 10.3390/sym14061223] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
This article reflects on the Klein–Gordon model, which frequently arises in the fields of solid-state physics and quantum field theories. We analytically delve into solitons and composite rogue-type wave propagation solutions of the model via the generalized Kudryashov and the extended Sinh Gordon expansion approaches. We obtain a class of analytically exact solutions in the forms of exponential and hyperbolic functions involving some arbitrary parameters with the help of Maple, which included comparing symmetric and non-symmetric solutions with other methods. After analyzing the dynamical behaviors, we caught distinct conditions on the accessible parameters of the solutions for the model. By applying conditions to the existing parameters, we obtained various types of rogue waves, bright and dark bells, combing bright–dark, combined dark–bright bells, kink and anti-kink solitons, and multi-soliton solutions. The nature of the solitons is geometrically explained for particular choices of the arbitrary parameters. It is indicated that the nonlinear rogue-type wave packets are restricted in two dimensions that characterized the rogue-type wave envelopes.
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8
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Maksymov IS, Huy Nguyen BQ, Pototsky A, Suslov S. Acoustic, Phononic, Brillouin Light Scattering and Faraday Wave-Based Frequency Combs: Physical Foundations and Applications. SENSORS (BASEL, SWITZERLAND) 2022; 22:3921. [PMID: 35632330 PMCID: PMC9143010 DOI: 10.3390/s22103921] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Revised: 05/16/2022] [Accepted: 05/20/2022] [Indexed: 11/16/2022]
Abstract
Frequency combs (FCs)-spectra containing equidistant coherent peaks-have enabled researchers and engineers to measure the frequencies of complex signals with high precision, thereby revolutionising the areas of sensing, metrology and communications and also benefiting the fundamental science. Although mostly optical FCs have found widespread applications thus far, in general FCs can be generated using waves other than light. Here, we review and summarise recent achievements in the emergent field of acoustic frequency combs (AFCs), including phononic FCs and relevant acousto-optical, Brillouin light scattering and Faraday wave-based techniques that have enabled the development of phonon lasers, quantum computers and advanced vibration sensors. In particular, our discussion is centred around potential applications of AFCs in precision measurements in various physical, chemical and biological systems in conditions where using light, and hence optical FCs, faces technical and fundamental limitations, which is, for example, the case in underwater distance measurements and biomedical imaging applications. This review article will also be of interest to readers seeking a discussion of specific theoretical aspects of different classes of AFCs. To that end, we support the mainstream discussion by the results of our original analysis and numerical simulations that can be used to design the spectra of AFCs generated using oscillations of gas bubbles in liquids, vibrations of liquid drops and plasmonic enhancement of Brillouin light scattering in metal nanostructures. We also discuss the application of non-toxic room-temperature liquid-metal alloys in the field of AFC generation.
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Affiliation(s)
- Ivan S. Maksymov
- Optical Sciences Centre, Swinburne University of Technology, Hawthorn, VIC 3122, Australia;
| | - Bui Quoc Huy Nguyen
- Optical Sciences Centre, Swinburne University of Technology, Hawthorn, VIC 3122, Australia;
| | - Andrey Pototsky
- Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122, Australia; (A.P.); (S.S.)
| | - Sergey Suslov
- Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122, Australia; (A.P.); (S.S.)
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9
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Varshney V, Kumarasamy S, Mishra A, Biswal B, Prasad A. Traveling of extreme events in network of counter-rotating nonlinear oscillators. CHAOS (WOODBURY, N.Y.) 2021; 31:093136. [PMID: 34598461 DOI: 10.1063/5.0059750] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 08/30/2021] [Indexed: 06/13/2023]
Abstract
We study the propagation of rare or extreme events in a network of coupled nonlinear oscillators, where counter-rotating oscillators play the role of the malfunctioning agents. The extreme events originate from the coupled counter-oscillating pair of oscillators through a mechanism of saddle-node bifurcation. A detailed study of the propagation and the destruction of the extreme events and how these events depend on the strength of the coupling is presented. Extreme events travel only when nearby oscillators are in synchronization. The emergence of extreme events and their propagation are observed in a number of excitable systems for different network sizes and for different topologies.
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Affiliation(s)
- Vaibhav Varshney
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Suresh Kumarasamy
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
| | - Ajay Mishra
- Department of Physics, Dyal Singh College, University of Delhi, Delhi 110003, India
| | - Bibhu Biswal
- Cluster Innovation Centre, University of Delhi, Delhi 110007, India
| | - Awadhesh Prasad
- Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India
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10
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Abstract
The modulational instability of ion-acoustic waves (IAWs) in a four-component magneto-plasma system consisting of positive–negative ions fluids and non-Maxwellian (r,q) distributed electrons and positrons, is investigated. The basic system of fluid equations is reduced to a three-dimensional (3D) nonlinear Schrödinger Equation (NLS). The domains of the IAWs stability are determined and are found to be strongly affected by electrons and positrons spectral parameters r and q and temperature ratio Tp/Te (Tp and Te are positrons and electrons temperatures, respectively). The existence domains, where we can observe the ion-acoustic rogue waves (IARWs) are determined. The basic features of IARWs are analyzed numerically against the distribution parameters and the other system physical parameters as Tp/Te and the external magnetic field strength. Moreover, a comparison between the first- and second-order rogue waves solution is presented. Our results show that the nonlinearity of the system increases by increasing the values of the non-Maxwellian parameters and the physical parameters of the system. This means that the system gains more energy by increasing r, q, Tp, and the external magnetic field through the cyclotron frequency ωci. Finally, our theoretical model displays the effect of the non-Maxwellian particles on the MI of the IAWs and RWs and its importance in D–F regions of Earth’s ionosphere through (H+,O2−) and (H+,H−) electronegative plasmas.
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11
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Zhang HQ, Chen F. Rogue waves for the fourth-order nonlinear Schrödinger equation on the periodic background. CHAOS (WOODBURY, N.Y.) 2021; 31:023129. [PMID: 33653045 DOI: 10.1063/5.0030072] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Accepted: 02/01/2021] [Indexed: 06/12/2023]
Abstract
In this paper, we construct rogue wave solutions on the periodic background for the fourth-order nonlinear Schrödinger (NLS) equation. First, we consider two types of the Jacobi elliptic function solutions, i.e., dn- and cn-function solutions. Both dn- and cn-periodic waves are modulationally unstable with respect to the long-wave perturbations. Second, on the background of both periodic waves, we derive rogue wave solutions by combining the method of nonlinearization of spectral problem with the Darboux transformation method. Furthermore, by the study of the dynamics of rogue waves, we find that they have the analogs in the standard NLS equation, and the higher-order effects do not have effect on the magnification factor of rogue waves. In addition, when the elliptic modulus approaches 1, rogue wave solutions can reduce to multi-pole soliton solutions in which the interacting solitons form weakly bound states.
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Affiliation(s)
- Hai-Qiang Zhang
- College of Science, University of Shanghai for Science and Technology, P. O. Box 253, Shanghai 200093, China
| | - Fa Chen
- College of Science, University of Shanghai for Science and Technology, P. O. Box 253, Shanghai 200093, China
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12
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Gao L, Wu Q, Cao Y, Wabnitz S, Zhu T. Optical polarization rogue waves and their identifications. JPHYS PHOTONICS 2020. [DOI: 10.1088/2515-7647/ab9bf7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Optical rogue waves are a class of pulses with extremely large amplitudes, whose probability of occurrence unexpectedly deviates from Gaussian-law statistics. To date, the mechanisms of rogue wave generation are still debated: investigations are under way, exploring the statistics of various pulse dimensions across different physical domains. Although polarization is one of the fundamental parameters of optical rogue waves, its statistics have received little attention until recently. Here, we review recent process of the polarization-dependent properties of optical rogue waves in ultrafast optics. Based on a two-dimensional statistical model, we introduce the concept of optical polarization rogue waves. Specifically, we consider the frequency of generation of waves with freak or rogue state of polarization, with a probability of occurrence deviating from a normal distribution. We demonstrate three nonlinear optical laser systems: a partially mode-locked laser, a dissipative soliton laser, and supercontinuum generation within a highly nonlinear fiber. Further, we identify optical polarization rogue waves in nonlinear laser systems, and discuss their generation mechanisms. Related results reveal that optical polarization rogue waves are embedded in optical systems with a deteriorated degree of coherence, which originates from vector four-wave-mixing processes. Polarization-dependent investigations will provide additional insight for our understanding of optical rogue waves.
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13
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Maksymov IS, Pototsky A. Excitation of Faraday-like body waves in vibrated living earthworms. Sci Rep 2020; 10:8564. [PMID: 32444625 PMCID: PMC7244598 DOI: 10.1038/s41598-020-65295-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2020] [Accepted: 04/28/2020] [Indexed: 12/03/2022] Open
Abstract
Biological cells and many living organisms are mostly made of liquids and therefore, by analogy with liquid drops, they should exhibit a range of fundamental nonlinear phenomena such as the onset of standing surface waves. Here, we test four common species of earthworm to demonstrate that vertical vibration of living worms lying horizontally on a flat solid surface results in the onset of subharmonic Faraday-like body waves, which is possible because earthworms have a hydrostatic skeleton with a flexible skin and a liquid-filled body cavity. Our findings are supported by theoretical analysis based on a model of parametrically excited vibrations in liquid-filled elastic cylinders using material parameters of the worm's body reported in the literature. The ability to excite nonlinear subharmonic body waves in a living organism could be used to probe, and potentially to control, important biophysical processes such as the propagation of nerve impulses, thereby opening up avenues for addressing biological questions of fundamental impact.
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Affiliation(s)
- Ivan S Maksymov
- Centre for Micro-Photonics, Swinburne University of Technology, Hawthorn, Victoria, 3122, Australia.
| | - Andrey Pototsky
- Department of Mathematics, Faculty of Science Engineering and Technology, Swinburne University of Technology, Hawthorn, Victoria, 3122, Australia.
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14
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Maksymov IS, Pototsky A. Harmonic and subharmonic waves on the surface of a vibrated liquid drop. Phys Rev E 2019; 100:053106. [PMID: 31869993 DOI: 10.1103/physreve.100.053106] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2019] [Indexed: 11/07/2022]
Abstract
Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry, and photonics. Here we study, theoretically and experimentally, the response of pancake-shaped liquid drops supported by a solid plate that vertically vibrates at a single, low acoustic range frequency. When the vibration amplitudes are small, the primary response of the drop is harmonic at the frequency of the vibration. However, as the amplitude increases, the half-frequency subharmonic Faraday waves are excited parametrically on the drop surface. We develop a simple hydrodynamic model of a one-dimensional liquid drop to analytically determine the amplitudes of the harmonic and the first superharmonic components of the linear response of the drop. In the nonlinear regime, our numerical analysis reveals an intriguing cascade of instabilities leading to the onset of subharmonic Faraday waves, their modulation instability, and chaotic regimes with broadband power spectra. We show that the nonlinear response is highly sensitive to the ratio of the drop size and Faraday wavelength. The primary bifurcation of the harmonic waves is shown to be dominated by a period-doubling bifurcation, when the drop height is comparable with the width of the viscous boundary layer. Experimental results conducted using low-viscosity ethanol and high-viscocity canola oil drops vibrated at 70Hz are in qualitative agreement with the predictions of our modeling.
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Affiliation(s)
- Ivan S Maksymov
- Centre for Micro-Photonics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
| | - Andrey Pototsky
- Department of Mathematics, Faculty of Science Engineering and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia
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15
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Kengne E, Liu WM. Transmission of rogue wave signals through a modified Noguchi electrical transmission network. Phys Rev E 2019; 99:062222. [PMID: 31330672 DOI: 10.1103/physreve.99.062222] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2019] [Indexed: 11/07/2022]
Abstract
A distributed electrical transmission network with dispersive elements that consists of a large number of identical unit cells is considered. Using the reductive perturbation method in the semidiscrete limit, we show that the voltage for the network is described by a nonlinear Schrödinger (NLS) equation with an external linear potential. Using such a NLS equation, the propagation of the first- and second-order rogue waves in the system is predicted and analyzed quantitatively and qualitatively. The rogue waves are expected to propagate for the bandwidth frequencies where the network may exhibit modulational instability. The effects of relevant network parameters on the characteristics of the rogue wave parameters are investigated. We show how to manipulate the relevant network parameters as well as the propagating frequency either to amplify the propagation of the rogue waves through the network, or to prevent rogue waves from being amplified in the network under consideration.
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Affiliation(s)
- E Kengne
- Laboratory of Advanced Microsystems Engineering, Department of Computer Science and Engineering, University of Quebec at Outaouais, 101 St.-Jean-Bosco, Succursale Hull, Gatineau (PQ), Canada J8Y 3G5.,Laboratory of Condensed Matter Theory and Materials Computation, Institute of Physics, Chinese Academy of Sciences, No. 8 South-Three Street, ZhongGuanCun, Beijing 100190, China
| | - W M Liu
- Laboratory of Condensed Matter Theory and Materials Computation, Institute of Physics, Chinese Academy of Sciences, No. 8 South-Three Street, ZhongGuanCun, Beijing 100190, China
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16
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Huang X, Dong H, Liu Z, Zhao YP. Probing Micro-Newton Forces on Solid/Liquid/Gas Interfaces Using Transmission Phase Shift. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:5442-5447. [PMID: 30916566 DOI: 10.1021/acs.langmuir.8b03922] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Many of the nature and life systems are driven by capillary interactions on solid/liquid/gas interfaces. Here, we present a profilometry technique called transmission phase shift for visualizing the liquid/gas interfaces in three dimensions with high resolution. Using this approach, we probe the change in tiny forces with particle radius at a solid/liquid/gas interface. We provide the first direct evidence that in the issues of floating versus sinking at small-scale, Archimedes' principle should be generalized to include the crucial role of surface tension and reveal the dominant regimes of floating particles based on the Bond number. Remarkably, the measured forces are in the range of micro-Newtons, suggesting that this terse methodology may guide the future design of a liquid microbalance and will be a universal tool for investigating capillarity and interface issues.
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Affiliation(s)
- Xianfu Huang
- State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics , Chinese Academy of Sciences , Beijing 100190 , China
- School of Aerospace Engineering , Beijing Institute of Technology , Beijing 100081 , China
- School of Engineering Science , University of Chinese Academy of Sciences , Beijing 100049 , China
| | - Huimin Dong
- School of Aerospace Engineering , Beijing Institute of Technology , Beijing 100081 , China
| | - Zhanwei Liu
- School of Aerospace Engineering , Beijing Institute of Technology , Beijing 100081 , China
| | - Ya-Pu Zhao
- State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics , Chinese Academy of Sciences , Beijing 100190 , China
- School of Engineering Science , University of Chinese Academy of Sciences , Beijing 100049 , China
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17
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Han JF, Liang T, Duan WS. Possibility of the existence of the rogue wave and the super rogue wave in granular matter. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:5. [PMID: 30656485 DOI: 10.1140/epje/i2019-11764-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2018] [Accepted: 12/10/2018] [Indexed: 06/09/2023]
Abstract
By using the traditional perturbation technique, a focusing nonlinear Schrödinger equation (NLSE) for the one-dimensional bead chain with the initial prestress is first obtained. The Peregrine soliton, called the rogue wave in the present paper, and the super rogue wave are investigated both numerically and analytically. It is noted that both the rogue wave and the super rogue wave do exist in the one-dimensional bead chain. The solutions from the NLSE can correctly describe the real rogue wave as well as the real super rogue wave in the limiting case of small amplitude. Both the rogue wave and the super rogue wave propagate in the granular bead chain as if they are solitary waves.
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Affiliation(s)
- Juan-Fang Han
- College of Physics and Electronic Engineering, Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China
- Joint Laboratory of Atomic and Molecular Physics of NWNU &IMP CAS, Northwest Normal University, 730070, Lanzhou, China
| | - Tao Liang
- College of Physics and Electronic Engineering, Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China.
- Joint Laboratory of Atomic and Molecular Physics of NWNU &IMP CAS, Northwest Normal University, 730070, Lanzhou, China.
| | - Wen-Shan Duan
- College of Physics and Electronic Engineering, Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China
- Joint Laboratory of Atomic and Molecular Physics of NWNU &IMP CAS, Northwest Normal University, 730070, Lanzhou, China
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18
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Hu X, Cubaud T. Viscous Wave Breaking and Ligament Formation in Microfluidic Systems. PHYSICAL REVIEW LETTERS 2018; 121:044502. [PMID: 30095958 DOI: 10.1103/physrevlett.121.044502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Revised: 06/13/2018] [Indexed: 06/08/2023]
Abstract
Rapid layering of viscous materials in microsystems encompasses a range of hydrodynamic instabilities that facilitate mixing and emulsification processes of fluids having large differences in viscosity. We experimentally study the stability of high-viscosity stratifications made of miscible and immiscible fluid pairs in square microchannels and characterize the propagation dynamics of interfacial waves, including breaking and viscous ligament entrainment from wave crests at moderate Reynolds numbers. For large viscosity contrasts, parallel fluid streams adopt widely different velocities and provide a simple model system to probe the role of inflectional instabilities of stratified microflows in relation with classic inviscid-stability theory. We reveal novel viscous wave regimes and unravel dispersion relationships in the presence and absence of interfacial tension. Detailed examination of wave celerity shows the existence of optimal operation conditions for passively disturbing miscible fluid flows and continuously dispersing low-and high-viscosity fluids at the small scale.
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Affiliation(s)
- Xiaoyi Hu
- Department of Mechanical Engineering, Stony Brook University, Stony Brook, New York 11794, USA
| | - Thomas Cubaud
- Department of Mechanical Engineering, Stony Brook University, Stony Brook, New York 11794, USA
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Lee S, Park K, Kim H, Vazquez-Zuniga LA, Kim J, Jeong Y. Intermittent burst of a super rogue wave in the breathing multi-soliton regime of an anomalous fiber ring cavity. OPTICS EXPRESS 2018; 26:11447-11457. [PMID: 29716063 DOI: 10.1364/oe.26.011447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2018] [Accepted: 04/14/2018] [Indexed: 06/08/2023]
Abstract
We report the intermittent burst of a super rogue wave in the multi-soliton (MS) regime of an anomalous-dispersion fiber ring cavity. We exploit the spatio-temporal measurement technique to log and capture the shot-to-shot wave dynamics of various pulse events in the cavity, and obtain the corresponding intensity probability density function, which eventually unveils the inherent nature of the extreme events encompassed therein. In the breathing MS regime, a specific MS regime with heavy soliton population, the natural probability of pulse interaction among solitons and dispersive waves exponentially increases owing to the extraordinarily high soliton population density. Combination of the probabilistically started soliton interactions and subsequently accompanying dispersive waves in their vicinity triggers an avalanche of extreme events with even higher intensities, culminating to a burst of a super rogue wave nearly ten times stronger than the average solitons observed in the cavity. Without any cavity modification or control, the process naturally and intermittently recurs within a time scale in the order of ten seconds.
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20
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Liu W, Zhang J, Li X. Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation. PLoS One 2018; 13:e0192281. [PMID: 29432495 PMCID: PMC5809061 DOI: 10.1371/journal.pone.0192281] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Accepted: 01/19/2018] [Indexed: 11/18/2022] Open
Abstract
In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.
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Affiliation(s)
- Wei Liu
- College of Mathematic and Information Science, Shandong Technology and Business University, Yantai, 264005, P. R. China
| | - Jing Zhang
- Chuo College of Technology, Tokyo, 114-8543, Japan
| | - Xiliang Li
- College of Mathematic and Information Science, Shandong Technology and Business University, Yantai, 264005, P. R. China
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21
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Liu J, Hang C, Huang G. Weak-light vector rogue waves, breathers, and their Stern-Gerlach deflection via electromagnetically induced transparency. OPTICS EXPRESS 2017; 25:23408-23423. [PMID: 29041642 DOI: 10.1364/oe.25.023408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2017] [Accepted: 07/23/2017] [Indexed: 06/07/2023]
Abstract
We propose a scheme for generating and manipulating vector (or two-component) optical rogue waves using Akhmediev and Kuznetsov-Ma breathers in a coherent atomic system with an M-type five-level configuration via electromagnetically induced transparency (EIT). We show that the propagation velocity of these nonlinear excitations can be reduced to 10-4c and their generation power can be lowered to microwatts. We also show that the motion trajectories of the two polarization components in these excitations can be deflected significantly by using a transversal gradient magnetic field, similar to the Stern-Gerlach effect of an atomic beam. We find that the deflection angle can reach to 10-4 radian within the propagation distance of only several centimeters; at variance with the atomic Stern-Gerlach effect, the deflection angle can be made different for different polarization components and may be actively adjusted in a controllable way. The results obtained may have promising applications, including the precise measurement of gradient magnetic fields.
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22
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Monroy F. Surface hydrodynamics of viscoelastic fluids and soft solids: Surfing bulk rheology on capillary and Rayleigh waves. Adv Colloid Interface Sci 2017; 247:4-22. [PMID: 28735885 DOI: 10.1016/j.cis.2017.07.006] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2017] [Revised: 07/09/2017] [Accepted: 07/09/2017] [Indexed: 11/18/2022]
Abstract
From the recent advent of the new soft-micro technologies, the hydrodynamic theory of surface modes propagating on viscoelastic bodies has reinvigorated this field of technology with interesting predictions and new possible applications, so recovering its scientific interest very limited at birth to the academic scope. Today, a myriad of soft small objects, deformable meso- and micro-structures, and macroscopically viscoelastic bodies fabricated from colloids and polymers are already available in the materials catalogue. Thus, one can envisage a constellation of new soft objects fabricated by-design with a functional dynamics based on the mechanical interplay of the viscoelastic material with the medium through their interfaces. In this review, we recapitulate the field from its birth and theoretical foundation in the latest 1980s up today, through its flourishing in the 90s from the prediction of extraordinary Rayleigh modes in coexistence with ordinary capillary waves on the surface of viscoelastic fluids, a fact first confirmed in experiments by Dominique Langevin and me with soft gels [Monroy and Langevin, Phys. Rev. Lett. 81, 3167 (1998)]. With this observational discovery at sight, we not only settled the theory previously formulated a few years before, but mainly opened a new field of applications with soft materials where the mechanical interplay between surface and bulk motions matters. Also, new unpublished results from surface wave experiments performed with soft colloids are reported in this contribution, in which the analytic methods of wave surfing synthetized together with the concept of coexisting capillary-shear modes are claimed as an integrated tool to insightfully scrutinize the bulk rheology of soft solids and viscoelastic fluids. This dedicatory to the figure of Dominique Langevin includes an appraisal of the relevant theoretical aspects of the surface hydrodynamics of viscoelastic fluids, and the coverage of the most important experimental results obtained during the three decades of research on this field.
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Affiliation(s)
- Francisco Monroy
- Departamento de Química Física I, Facultad de Química, Universidad Complutense de Madrid, E28040 Madrid, Spain; Unit of Traslational Biophysics, Instituto de Investigación Sanitaria Hospital 12 de Octubre (imas12), E28041 Madrid, Spain.
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23
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Cuevas-Maraver J, Kevrekidis PG, Frantzeskakis DJ, Karachalios NI, Haragus M, James G. Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves. Phys Rev E 2017; 96:012202. [PMID: 29347195 DOI: 10.1103/physreve.96.012202] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2017] [Indexed: 06/07/2023]
Abstract
In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events. Given the space-time localized nature of Peregrine solitons, this is a priori a nontrivial task. Our main tool in this effort will be the study of the spectral stability of the periodic generalization of the Peregrine soliton in the evolution variable, namely the Kuznetsov-Ma breather. Given the periodic structure of the latter, we compute the corresponding Floquet multipliers, and examine them in the limit where the period of the orbit tends to infinity. This way, we extrapolate towards the stability of the limiting structure, namely the Peregrine soliton. We find that multiple unstable modes of the background are enhanced, yet no additional unstable eigenmodes arise as the Peregrine limit is approached. We explore the instability evolution also in direct numerical simulations.
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Affiliation(s)
- J Cuevas-Maraver
- Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, Escuela Politécnica Superior, C/ Virgen de África, 7, 41011-Sevilla, Spain and Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis, Avenida Reina Mercedes s/n, 41012-Sevilla, Spain
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003-4515, USA
| | - D J Frantzeskakis
- Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
| | - N I Karachalios
- Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece
| | - M Haragus
- Institut FEMTO-ST, Département OPTIQUE, Université Bourgogne Franche-Comté, 25030 Besançon Cedex, France
| | - G James
- INRIA Grenoble - Rhône-Alpes, Bipop Team-Project, Inovallée, 655 Avenue de l'Europe, 38334 Saint Ismier Cedex, France
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24
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Zhang G, Yan Z, Wen XY. Modulational instability, beak-shaped rogue waves, multi-dark-dark solitons and dynamics in pair-transition-coupled nonlinear Schrödinger equations. Proc Math Phys Eng Sci 2017; 473:20170243. [PMID: 28804266 PMCID: PMC5549574 DOI: 10.1098/rspa.2017.0243] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2017] [Accepted: 06/23/2017] [Indexed: 11/12/2022] Open
Abstract
The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N-fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.
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Affiliation(s)
- Guoqiang Zhang
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Xiao-Yong Wen
- Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- Department of Mathematics, School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, People's Republic of China
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25
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Zhang H, Yang Y, Hong XR, Qi X, Duan WS, Yang L. Freak oscillation in a dusty plasma. Phys Rev E 2017; 95:053207. [PMID: 28618565 DOI: 10.1103/physreve.95.053207] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Indexed: 11/07/2022]
Abstract
The freak oscillation in one-dimensional dusty plasma is studied numerically by particle-in-cell method. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the rogue waves in dusty plasma. Additionally, the application scope of the analytical solution of the rogue wave described by the NLSE is given.
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Affiliation(s)
- Heng Zhang
- Northwest Normal University, Lanzhou 730070, China
| | - Yang Yang
- Northwest Normal University, Lanzhou 730070, China
| | - Xue-Ren Hong
- Northwest Normal University, Lanzhou 730070, China
| | - Xin Qi
- Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
| | | | - Lei Yang
- Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.,Department of Physics, Lanzhou University, Lanzhou 730000, China
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26
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Abstract
The generation of rogue waves is investigated in a class of nonlocal nonlinear Schrödinger (NLS) equations. In this system, modulation instability is suppressed as the effect of nonlocality increases. Despite this fact, there is a parameter regime where the number and amplitude of the rogue events increase as compared to the standard NLS equation, which is a limit of the system when nonlocality vanishes. Furthermore, the nature of these waves is investigated; while no analytical solutions are known to model these events, it is shown, numerically, that these rogue events differ significantly from the rational soliton (Peregrine) solution of the limiting NLS equation. The universal structure of the associated rogue waves is discussed and a local description is presented. These results can help in the experimental realization of rogue waves in these media.
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Affiliation(s)
| | - Mark J Ablowitz
- Department of Applied Mathematics, University of Colorado, 526 UCB, Boulder, Colorado 80309-0526, USA
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27
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Toffoli A, Proment D, Salman H, Monbaliu J, Frascoli F, Dafilis M, Stramignoni E, Forza R, Manfrin M, Onorato M. Wind Generated Rogue Waves in an Annular Wave Flume. PHYSICAL REVIEW LETTERS 2017; 118:144503. [PMID: 28430520 DOI: 10.1103/physrevlett.118.144503] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Indexed: 06/07/2023]
Abstract
We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment.
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Affiliation(s)
- A Toffoli
- Department of Infrastructure Engineering, The University of Melbourne, Parkville VIC 3010, Australia
| | - D Proment
- School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
| | - H Salman
- School of Mathematics, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
| | - J Monbaliu
- K.U. Leuven, Kasteelpark Arenberg 40, 3001 Heverlee, Belgium
| | - F Frascoli
- Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn VIC 3122, Australia
| | - M Dafilis
- Department of Health and Medical Sciences, Faculty of Health, Art, and Design, Swinburne University of Technology, Hawthorn VIC 3122, Australia
| | - E Stramignoni
- Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| | - R Forza
- Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| | - M Manfrin
- Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
| | - M Onorato
- Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
- INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
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28
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Michel G, Pétrélis F, Fauve S. Observation of Thermal Equilibrium in Capillary Wave Turbulence. PHYSICAL REVIEW LETTERS 2017; 118:144502. [PMID: 28430497 DOI: 10.1103/physrevlett.118.144502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Indexed: 06/07/2023]
Abstract
We investigate capillary wave turbulence at scales larger than the forcing one. At such scales, our measurements show that the surface waves dynamics is the one of a thermal equilibrium state in which the effective temperature is related to the injected power. We characterize this evolution with a scaling law and report the statistical properties of the large-scale surface elevation depending on this effective temperature.
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Affiliation(s)
- Guillaume Michel
- Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, Université P. et M. Curie, Université Paris Diderot, Paris 75005, France
| | - François Pétrélis
- Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, Université P. et M. Curie, Université Paris Diderot, Paris 75005, France
| | - Stéphan Fauve
- Laboratoire de Physique Statistique, École Normale Supérieure, CNRS, Université P. et M. Curie, Université Paris Diderot, Paris 75005, France
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29
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Shen Y, Kevrekidis PG, Veldes GP, Frantzeskakis DJ, DiMarzio D, Lan X, Radisic V. From solitons to rogue waves in nonlinear left-handed metamaterials. Phys Rev E 2017; 95:032223. [PMID: 28415369 DOI: 10.1103/physreve.95.032223] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2016] [Indexed: 06/07/2023]
Abstract
In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.
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Affiliation(s)
- Yannan Shen
- Department of Mathematics and Statistics, California State University, Northridge, California 91330, USA
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
| | - G P Veldes
- Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
- Department of Electronics Engineering, Technological Educational Institute of Central Greece, Lamia 35100, Greece
| | - D J Frantzeskakis
- Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
| | - D DiMarzio
- NG Next, Northrop Grumman Corporation, One Space Park, Redondo Beach, California 90278, USA
| | - X Lan
- NG Next, Northrop Grumman Corporation, One Space Park, Redondo Beach, California 90278, USA
| | - V Radisic
- NG Next, Northrop Grumman Corporation, One Space Park, Redondo Beach, California 90278, USA
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30
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Pierangeli D, Di Mei F, Di Domenico G, Agranat AJ, Conti C, DelRe E. Turbulent Transitions in Optical Wave Propagation. PHYSICAL REVIEW LETTERS 2016; 117:183902. [PMID: 27834998 DOI: 10.1103/physrevlett.117.183902] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Indexed: 06/06/2023]
Abstract
We report the direct observation of the onset of turbulence in propagating one-dimensional optical waves. The transition occurs as the disordered hosting material passes from being linear to one with extreme nonlinearity. As the response grows, increased wave interaction causes a modulational unstable quasihomogeneous flow to be superseded by a chaotic and spatially incoherent one. Statistical analysis of high-resolution wave behavior in the turbulent regime unveils the emergence of concomitant rogue waves. The transition, observed in a photorefractive ferroelectric crystal, introduces a new and rich experimental setting for the study of optical wave turbulence and information transport in conditions dominated by large fluctuations and extreme nonlinearity.
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Affiliation(s)
- D Pierangeli
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
| | - F Di Mei
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
| | - G Di Domenico
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
- Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, 00161 Rome, Italy
| | - A J Agranat
- Applied Physics Department, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - C Conti
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
- ISC-CNR, Università di Roma "La Sapienza," 00185 Rome, Italy
| | - E DelRe
- Dipartimento di Fisica, Università di Roma "La Sapienza," 00185 Rome, Italy
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31
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Liu M, Luo AP, Xu WC, Luo ZC. Dissipative rogue waves induced by soliton explosions in an ultrafast fiber laser. OPTICS LETTERS 2016; 41:3912-3915. [PMID: 27607935 DOI: 10.1364/ol.41.003912] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We reported on the observation of dissipative rogue waves (DRWs) induced by soliton explosions in an ultrafast fiber laser. It was found that the soliton explosions could be obtained in the fiber laser at a critical pump power level. During the process of the soliton explosion, the high-amplitude waves that fulfill the rogue wave criteria could be detected. The appearance of the DRWs was identified by characterizing the intensity statistics of the time-stretched soliton profile based on the dispersive Fourier-transform method. Our findings provide the first experimental demonstration that the DRWs could be observed in the soliton explosion regime and further enhance the understanding of the physical mechanism of optical RW generation.
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32
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Denner F. Frequency dispersion of small-amplitude capillary waves in viscous fluids. Phys Rev E 2016; 94:023110. [PMID: 27627395 DOI: 10.1103/physreve.94.023110] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2016] [Indexed: 11/07/2022]
Abstract
This work presents a detailed study of the dispersion of capillary waves with small amplitude in viscous fluids using an analytically derived solution to the initial value problem of a small-amplitude capillary wave as well as direct numerical simulation. A rational parametrization for the dispersion of capillary waves in the underdamped regime is proposed, including predictions for the wave number of critical damping based on a harmonic-oscillator model. The scaling resulting from this parametrization leads to a self-similar solution of the frequency dispersion of capillary waves that covers the entire underdamped regime, which allows an accurate evaluation of the frequency at a given wave number, irrespective of the fluid properties. This similarity also reveals characteristic features of capillary waves, for instance that critical damping occurs when the characteristic time scales of dispersive and dissipative mechanisms are balanced. In addition, the presented results suggest that the widely adopted hydrodynamic theory for damped capillary waves does not accurately predict the dispersion when viscous damping is significant, and an alternative definition of the damping rate, which provides consistent accuracy in the underdamped regime, is presented.
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Affiliation(s)
- Fabian Denner
- Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
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33
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Temgoua DDE, Kofane TC. Influence of optical activity on rogue waves propagating in chiral optical fibers. Phys Rev E 2016; 93:062223. [PMID: 27415269 DOI: 10.1103/physreve.93.062223] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2016] [Indexed: 11/07/2022]
Abstract
We derive the nonlinear Schrödinger (NLS) equation in chiral optical fiber with right- and left-hand nonlinear polarization. We use the similarity transformation to reduce the generalized chiral NLS equation to the higher-order integrable Hirota equation. We present the first- and second-order rational solutions of the chiral NLS equation with variable and constant coefficients, based on the modified Darboux transformation method. For some specific set of parameters, the features of chiral optical rogue waves are analyzed from analytical results, showing the influence of optical activity on waves. We also generate the exact solutions of the two-component coupled nonlinear Schrödinger equations, which describe optical activity effects on the propagation of rogue waves, and their properties in linear and nonlinear coupling cases are investigated. The condition of modulation instability of the background reveals the existence of vector rogue waves and the number of stable and unstable branches. Controllability of chiral optical rogue waves is examined by numerical simulations and may bring potential applications in optical fibers and in many other physical systems.
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Affiliation(s)
- D D Estelle Temgoua
- Laboratory of Mechanics, Materials and Structures, Post Graduate School in Sciences, Technology and Geosciences, Doctoral Research Unit in Physics and Applications, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Organization for Women in Science for the Developing World, ICTP Campus, Strada Costiera 11, 34151 Trieste, Italy
| | - T C Kofane
- Laboratory of Mechanics, Materials and Structures, Post Graduate School in Sciences, Technology and Geosciences, Doctoral Research Unit in Physics and Applications, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon.,Centre d'Excellence Africain en Technologies de l'Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
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Manikandan K, Senthilvelan M. An analysis of spatiotemporal localized solutions in the variable coefficients (3 + 1)-dimensional nonlinear Schrödinger equation with six different forms of dispersion parameters. CHAOS (WOODBURY, N.Y.) 2016; 26:073116. [PMID: 27475076 DOI: 10.1063/1.4959145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields.
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Affiliation(s)
- K Manikandan
- Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India
| | - M Senthilvelan
- Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu, India
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Abdelghany AM, Abd El-Razek HN, Moslem WM, El-Labany SK. Solar wind implication on dust ion acoustic rogue waves. PHYSICS OF PLASMAS 2016; 23. [DOI: 10.1063/1.4954298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
The relevance of the solar wind with the magnetosphere of Jupiter that contains positively charged dust grains is investigated. The perturbation/excitation caused by streaming ions and electron beams from the solar wind could form different nonlinear structures such as rogue waves, depending on the dominant role of the plasma parameters. Using the reductive perturbation method, the basic set of fluid equations is reduced to modified Korteweg-de Vries (KdV) and further modified (KdV) equation. Assuming that the frequency of the carrier wave is much smaller than the ion plasma frequency, these equations are transformed into nonlinear Schrödinger equations with appropriate coefficients. Rational solution of the nonlinear Schrödinger equation shows that rogue wave envelopes are supported by the present plasma model. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming temperatures for both the ions and electrons. The dependence of the maximum rogue wave envelope amplitude on the system parameters has been investigated.
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Affiliation(s)
- A. M. Abdelghany
- Damietta University 1 Theoretical Physics Group, Department of Physics, Faculty of Science, , New Damietta 34517, Egypt
| | - H. N. Abd El-Razek
- Damietta University 1 Theoretical Physics Group, Department of Physics, Faculty of Science, , New Damietta 34517, Egypt
| | - W. M. Moslem
- Port Said University 2 Department of Physics, Faculty of Science, , Port Said 42521, Egypt
- The British University in Egypt (BUE) 3 Centre for Theoretical Physics, , El-Shorouk City, Cairo, Egypt
| | - S. K. El-Labany
- Damietta University 1 Theoretical Physics Group, Department of Physics, Faculty of Science, , New Damietta 34517, Egypt
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Manikandan K, Muruganandam P, Senthilvelan M, Lakshmanan M. Manipulating localized matter waves in multicomponent Bose-Einstein condensates. Phys Rev E 2016; 93:032212. [PMID: 27078349 DOI: 10.1103/physreve.93.032212] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2015] [Indexed: 11/07/2022]
Abstract
We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameters and external trap potentials through a similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures; namely, rogue waves, dark- and bright-soliton rogue waves, and rogue-wave breatherlike structures for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Furthermore, we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for the repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single-, two-, and three-composite rogue waves for three-component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.
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Affiliation(s)
- K Manikandan
- Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
| | - P Muruganandam
- Department of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
| | - M Senthilvelan
- Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
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Yahia ME, Tolba RE, El-Bedwehy NA, El-Labany SK, Moslem WM. Rogue waves lead to the instability in GaN semiconductors. Sci Rep 2015. [PMID: 26206731 PMCID: PMC4513275 DOI: 10.1038/srep12245] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
A new approach to understand the electron/hole interfaced plasma in GaN high electron mobility transistors (HEMTs). A quantum hydrodynamic model is constructed to include electrons/holes degenerate pressure, Bohm potential, and the exchange/correlation effect and then reduced to the nonlinear Schrödinger equation (NLSE). Numerical analysis of the latter predicts the rough (in)stability domains, which allow for the rogue waves to occur. Our results might give physical solution rather than the engineering one to the intrinsic problems in these high frequency/power transistors.
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Affiliation(s)
- M E Yahia
- 1] Faculty of Engineering and Natural Sciences, International University of Sarajevo (IUS), 71210, Ilidža, Sarajevo, Bosnia and Herzegovina [2] Center for Theoretical Physics, The British University in Egypt (BUE), El-Shorouk City, Cairo 11837, Egypt
| | - R E Tolba
- Department of Mathematics, Faculty of Science, Damietta University, New Damietta, 34517, Egypt
| | - N A El-Bedwehy
- Department of Mathematics, Faculty of Science, Damietta University, New Damietta, 34517, Egypt
| | - S K El-Labany
- Department of Physics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
| | - W M Moslem
- 1] Center for Theoretical Physics, The British University in Egypt (BUE), El-Shorouk City, Cairo 11837, Egypt [2] Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt
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38
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Klyatskin VI, Koshel KV. Anomalous sea surface structures as an object of statistical topography. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:063003. [PMID: 26172788 DOI: 10.1103/physreve.91.063003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Indexed: 06/04/2023]
Abstract
By exploiting ideas of statistical topography, we analyze the stochastic boundary problem of emergence of anomalous high structures on the sea surface. The kinematic boundary condition on the sea surface is assumed to be a closed stochastic quasilinear equation. Applying the stochastic Liouville equation, and presuming the stochastic nature of a given hydrodynamic velocity field within the diffusion approximation, we derive an equation for a spatially single-point, simultaneous joint probability density of the surface elevation field and its gradient. An important feature of the model is that it accounts for stochastic bottom irregularities as one, but not a single, perturbation. Hence, we address the assumption of the infinitely deep ocean to obtain statistic features of the surface elevation field and the squared elevation gradient field. According to the calculations, we show that clustering in the absolute surface elevation gradient field happens with the unit probability. It results in the emergence of rare events such as anomalous high structures and deep gaps on the sea surface almost in every realization of a stochastic velocity field.
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Affiliation(s)
- V I Klyatskin
- Obukhov Atmospheric Physics Institute of RAS, 3, Pyzhevsky per., Moscow 119017, Russia
| | - K V Koshel
- V.I.Il'ichev Pacific Oceanological Institute of RAS, 43, Baltiyskaya street, Vladivostok 690041, Russia Far Eastern Federal University 8, Sukhanova Street, Vladivostok, Russia Institute of Applied Mathematics of FEB RAS, 7, Radio Street, Vladivostok, Russia
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Abdurakhimov LV, Arefin M, Kolmakov GV, Levchenko AA, Lvov YV, Remizov IA. Bidirectional energy cascade in surface capillary waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023021. [PMID: 25768611 DOI: 10.1103/physreve.91.023021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2014] [Indexed: 06/04/2023]
Abstract
Based on an experiment and simulations, we report that an energy cascade in surface capillary waves can be bidirectional, that is, can simultaneously flow towards large and small wavelength scales from the pumping scales. The bidirectional energy cascade provides an effective global coupling mechanism between the scales. We show that formation of the bidirectional cascade leads to creation of large-scale, large-amplitude waves on the fluid surface.
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Affiliation(s)
- L V Abdurakhimov
- Institute of Solid State Physics RAS, Chernogolovka, Moscow Region 142432, Russia
- Okinawa Institute of Science and Technology, Okinawa 904-0495, Japan
| | - M Arefin
- Physics Department, New York City College of Technology, City University of New York, Brooklyn, New York 11201, USA
| | - G V Kolmakov
- Physics Department, New York City College of Technology, City University of New York, Brooklyn, New York 11201, USA
| | - A A Levchenko
- Institute of Solid State Physics RAS, Chernogolovka, Moscow Region 142432, Russia
| | - Yu V Lvov
- Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
| | - I A Remizov
- Institute of Solid State Physics RAS, Chernogolovka, Moscow Region 142432, Russia
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40
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Manikandan K, Muruganandam P, Senthilvelan M, Lakshmanan M. Manipulating matter rogue waves and breathers in Bose-Einstein condensates. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062905. [PMID: 25615162 DOI: 10.1103/physreve.90.062905] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2014] [Indexed: 06/04/2023]
Abstract
We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.
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Affiliation(s)
- K Manikandan
- Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
| | - P Muruganandam
- Department of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
| | - M Senthilvelan
- Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli 620024, Tamilnadu, India
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41
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Mareeswaran RB, Charalampidis EG, Kanna T, Kevrekidis PG, Frantzeskakis DJ. Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042912. [PMID: 25375572 DOI: 10.1103/physreve.90.042912] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2014] [Indexed: 06/04/2023]
Abstract
In this work we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.
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Affiliation(s)
- R Babu Mareeswaran
- Post Graduate and Research Department of Physics, Bishop Heber College, Tiruchirapalli-620 017, Tamil Nadu, India
| | - E G Charalampidis
- School of Civil Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece and Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
| | - T Kanna
- Post Graduate and Research Department of Physics, Bishop Heber College, Tiruchirapalli-620 017, Tamil Nadu, India
| | - P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
| | - D J Frantzeskakis
- Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
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42
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Randoux S, Walczak P, Onorato M, Suret P. Intermittency in integrable turbulence. PHYSICAL REVIEW LETTERS 2014; 113:113902. [PMID: 25259980 DOI: 10.1103/physrevlett.113.113902] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2014] [Indexed: 06/03/2023]
Abstract
We examine the statistical properties of nonlinear random waves that are ruled by the one-dimensional defocusing and integrable nonlinear Schrödinger equation. Using fast detection techniques in an optical fiber experiment, we observe that the probability density function of light fluctuations is characterized by tails that are lower than those predicted by a Gaussian distribution. Moreover, by applying a bandpass frequency optical filter, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian. These phenomena are very well described by numerical simulations of the one-dimensional nonlinear Schrödinger equation.
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Affiliation(s)
- Stéphane Randoux
- Laboratoire de Physique des Lasers, Atomes et Molecules, Université de Lille, UMR-CNRS 8523, France
| | - Pierre Walczak
- Laboratoire de Physique des Lasers, Atomes et Molecules, Université de Lille, UMR-CNRS 8523, France
| | - Miguel Onorato
- Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino, Italy and Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, 10125 Torino, Italy
| | - Pierre Suret
- Laboratoire de Physique des Lasers, Atomes et Molecules, Université de Lille, UMR-CNRS 8523, France
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43
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Chen S, Soto-Crespo JM, Grelu P. Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033203. [PMID: 25314555 DOI: 10.1103/physreve.90.033203] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2014] [Indexed: 06/04/2023]
Abstract
The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.
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Affiliation(s)
- Shihua Chen
- Department of Physics, Southeast University, Nanjing 211189, China
| | - Jose M Soto-Crespo
- Instituto de Óptica, Consejo Superior de Investigaciones Científicas (CSIC), Serrano 121, Madrid 28006, Spain
| | - Philippe Grelu
- Laboratoire Interdisciplinaire Carnot de Bourgogne, U.M.R. 6303 C.N.R.S., Université de Bourgogne, 9 avenue A. Savary, Boîte Postale 47870, Dijon Cedex 21078, France
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44
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Essama BGO, Atangana J, Frederick BM, Mokhtari B, Eddeqaqi NC, Kofane TC. Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032911. [PMID: 25314508 DOI: 10.1103/physreve.90.032911] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2014] [Indexed: 06/04/2023]
Abstract
We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.
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Affiliation(s)
- Bedel Giscard Onana Essama
- Laboratory of Electronics, Department of Physics, Faculty of Science, University of Yaounde I, P. O. Box 812, Yaounde, Cameroon and Department of Physics, Higher Teacher Training College Yaounde, University of Yaounde I, P. O. Box 47, Yaounde, Cameroon and Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC) Université de Yaoundé I, Cameroon
| | - Jacques Atangana
- Laboratory of Electronics, Department of Physics, Faculty of Science, University of Yaounde I, P. O. Box 812, Yaounde, Cameroon and Department of Physics, Higher Teacher Training College Yaounde, University of Yaounde I, P. O. Box 47, Yaounde, Cameroon and Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC) Université de Yaoundé I, Cameroon
| | - Biya Motto Frederick
- Laboratory of Electronics, Department of Physics, Faculty of Science, University of Yaounde I, P. O. Box 812, Yaounde, Cameroon
| | - Bouchra Mokhtari
- Department of Physics, Faculty of Science, Moulay Ismail University, P. O. Box 1120, Meknes, Morocco and Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC) Université de Yaoundé I, Cameroon
| | - Noureddine Cherkaoui Eddeqaqi
- Department of Physics, Faculty of Science, Moulay Ismail University, P. O. Box 1120, Meknes, Morocco and Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC) Université de Yaoundé I, Cameroon
| | - Timoleon Crepin Kofane
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P. O. Box 812, Yaounde, Cameroon and Centre d'Excellence Africain des Technologies de l'Information et de la Communication (CETIC) Université de Yaoundé I, Cameroon
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He J, Wang L, Li L, Porsezian K, Erdélyi R. Few-cycle optical rogue waves: complex modified Korteweg-de Vries equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062917. [PMID: 25019861 DOI: 10.1103/physreve.89.062917] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2014] [Indexed: 06/03/2023]
Abstract
In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-, and third-order rogue wave solutions and analyze the nature of evolution of higher-order rogue waves in detail. Based on detailed numerical and analytical investigations, we classify the higher-order rogue waves with respect to their intrinsic structure, namely, fundamental pattern, triangular pattern, and ring pattern. We also present several new patterns of the rogue wave according to the standard and nonstandard decomposition. The results of this paper explain the generalization of higher-order rogue waves in terms of rational solutions. We apply the contour line method to obtain the analytical formulas of the length and width of the first-order rogue wave of the complex mKdV and the nonlinear Schrödinger equations. In nonlinear optics, the higher-order rogue wave solutions found here will be very useful to generate high-power few-cycle optical pulses which will be applicable in the area of ultrashort pulse technology.
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Affiliation(s)
- Jingsong He
- Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
| | - Lihong Wang
- Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
| | - Linjing Li
- Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
| | - K Porsezian
- Department of Physics, Pondicherry University, Pondicherry 605014, India
| | - R Erdélyi
- Solar Physics and Space Plasma Research Centre, University of Sheffield, Sheffield S3 7RH, United Kingdom
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Kundu A, Mukherjee A, Naskar T. Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents. Proc Math Phys Eng Sci 2014; 470:20130576. [PMID: 24711719 PMCID: PMC3928955 DOI: 10.1098/rspa.2013.0576] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2013] [Accepted: 01/17/2014] [Indexed: 11/12/2022] Open
Abstract
Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.
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Affiliation(s)
| | - Abhik Mukherjee
- Theory Division, Saha Institute of Nuclear Physics, Kolkata, India
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47
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Chen S, Grelu P, Soto-Crespo JM. Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:011201. [PMID: 24580164 DOI: 10.1103/physreve.89.011201] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2013] [Indexed: 06/03/2023]
Abstract
Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.
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Affiliation(s)
- Shihua Chen
- Department of Physics, Southeast University, Nanjing 211189, China
| | - Philippe Grelu
- Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR No. 6303 associée au CNRS, Université de Bourgogne, 9 avenue A. Savary, BP 47870, Dijon Cedex 21078, France
| | - J M Soto-Crespo
- Instituto de Óptica, Consejo Superior de Investigaciones Científicas, Serrano 121, Madrid 28006, Spain
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48
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Loomba S, Kaur H. Optical rogue waves for the inhomogeneous generalized nonlinear Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062903. [PMID: 24483527 DOI: 10.1103/physreve.88.062903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2013] [Indexed: 06/03/2023]
Abstract
We present optical rogue wave solutions for a generalized nonlinear Schrodinger equation by using similarity transformation. We have predicted the propagation of rogue waves through a nonlinear optical fiber for three cases: (i) dispersion increasing (decreasing) fiber, (ii) periodic dispersion parameter, and (iii) hyperbolic dispersion parameter. We found that the rogue waves and their interactions can be tuned by properly choosing the parameters. We expect that our results can be used to realize improved signal transmission through optical rogue waves.
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Affiliation(s)
- Shally Loomba
- Department of Physics, Panjab University, Chandigarh 160014, India
| | - Harleen Kaur
- Department of Physics, Panjab University, Chandigarh 160014, India
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49
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Degasperis A, Lombardo S. Rational solitons of wave resonant-interaction models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052914. [PMID: 24329338 DOI: 10.1103/physreve.88.052914] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2013] [Indexed: 06/03/2023]
Abstract
Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find a broad family of such solutions of the three wave resonant interaction equations.
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Affiliation(s)
- Antonio Degasperis
- INFN, Dipartimento di Fisica, "Sapienza" Università di Roma, P. le A. Moro 2, 00185 Rome, Italy
| | - Sara Lombardo
- Mathematics and Information Sciences, Northumbria University, Newcastle, United Kingdom
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Baronio F, Conforti M, Degasperis A, Lombardo S. Rogue waves emerging from the resonant interaction of three waves. PHYSICAL REVIEW LETTERS 2013; 111:114101. [PMID: 24074089 DOI: 10.1103/physrevlett.111.114101] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2013] [Indexed: 06/02/2023]
Abstract
We introduce a novel family of analytic solutions of the three-wave resonant interaction equations for the purpose of modeling unique events, i.e., "amplitude peaks" which are isolated in space and time. The description of these solutions is likely to be a crucial step in the understanding and forecasting of rogue waves in a variety of multicomponent wave dynamics, from oceanography to optics and from plasma physics to acoustics.
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Affiliation(s)
- Fabio Baronio
- Dipartimento di Ingegneria dell'Informazione, Università di Brescia, Via Branze 38, 25123 Brescia, Italy
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