1
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Weng W. Large-space and large-time asymptotic properties of vector rogon-soliton and soliton-like solutions for n-component NLS equations. CHAOS (WOODBURY, N.Y.) 2024; 34:093115. [PMID: 39270071 DOI: 10.1063/5.0226548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2024] [Accepted: 08/14/2024] [Indexed: 09/15/2024]
Abstract
In this paper, we analyze the large-space and large-time asymptotic properties of the vector rogon-soliton and soliton-like solutions of the n-component nonlinear Schrödinger equation with mixed nonzero and zero boundary conditions. In particular, we find that these solutions have different decay velocities along different directions of the x axis, that is, the solutions exponentially and algebraically decay along the positive and negative directions of the x axis, respectively. Moreover, we study the change of the acceleration of soliton moving with the increase in time or distance along the characteristic line (i.e., soliton moving trajectory). As a result, we find that the product of the acceleration and distance square tends to some constant value as time increases. These results will be useful to better understand the related multi-wave phenomena and to design physical experiments.
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Affiliation(s)
- Weifang Weng
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China
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2
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Sun J, Dong H, Liu M, Fang Y. Data-driven rogue waves solutions for the focusing and variable coefficient nonlinear Schrödinger equations via deep learning. CHAOS (WOODBURY, N.Y.) 2024; 34:073134. [PMID: 39028903 DOI: 10.1063/5.0209068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 07/03/2024] [Indexed: 07/21/2024]
Abstract
In this paper, we investigate the data-driven rogue waves solutions of the focusing and the variable coefficient nonlinear Schrödinger (NLS) equations by the deep learning method from initial and boundary conditions. Specifically, first- and second-order rogue wave solutions for the focusing NLS equation and three deformed rogue wave solutions for the variable coefficient NLS equation are solved using physics-informed memory networks (PIMNs). The effects of optimization algorithm, network structure, and mesh size on the solution accuracy are discussed. Numerical experiments clearly demonstrate that the PIMNs can capture the nonlinear features of rogue waves solutions very well. This is of great significance for revealing the dynamical behavior of the rogue waves solutions and advancing the application of deep learning in the field of solving partial differential equations.
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Affiliation(s)
- Jiuyun Sun
- 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
| | - Mingshuo Liu
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
| | - Yong Fang
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
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3
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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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4
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Ge S, Liu C, Huang Y, Zhou P, Li N. Enhanced extreme events in three cascade-coupled semiconductor lasers. OPTICS EXPRESS 2024; 32:13906-13917. [PMID: 38859349 DOI: 10.1364/oe.517142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2023] [Accepted: 03/21/2024] [Indexed: 06/12/2024]
Abstract
Extreme events (EEs) are rare and unpredictable, as have been observed in nature. Up to now, manipulating EEs has remained a challenge. Here, we experimentally observe the enhancement of EEs in a three cascade-coupled semiconductor laser system. Specifically, a continuous-wave optical injection semiconductor laser acts as the chaotic source with rare EEs, which is subsequently injected into a second laser for increasing the number of EEs. Interestingly, we find that the number and region size of EEs can be further enhanced by sequentially injecting into a third laser, i.e., a cascade-injection structure. Our experimental observations are in good agreement with the numerical results, which indicate that EEs can be significantly enhanced in wide injection parameter space due to the cascade-injection effect. Furthermore, our simulations show that the evoluation of the regions with enhanced EEs may be associated with the noise considered.
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5
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Wen XY, Liu XK, Chen Y, Yan Z. Rogue wave excitations and hybrid wave structures of the Heisenberg ferromagnet equation with time-dependent inhomogeneous bilinear interaction and spin-transfer torque. CHAOS (WOODBURY, N.Y.) 2024; 34:033131. [PMID: 38502966 DOI: 10.1063/5.0191956] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2023] [Accepted: 02/19/2024] [Indexed: 03/21/2024]
Abstract
In this paper, we focus on the localized rational waves of the variable-coefficient Heisenberg spin chain equation, which models the local magnetization in ferromagnet with time-dependent inhomogeneous bilinear interaction and spin-transfer torque. First, we establish the iterative generalized (m,N-m)-fold Darboux transformation of the Heisenberg spin chain equation. Then, the novel localized rational solutions (LRSs), rogue waves (RWs), periodic waves, and hybrid wave structures on the periodic, zero, and nonzero constant backgrounds with the time-dependent coefficients α(t) and β(t) are obtained explicitly. Additionally, we provide the trajectory curves of magnetization and the variation of the magnetization direction for the obtained nonlinear waves at different times. These phenomena imply that the LRSs and RWs play the crucial roles in changing the circular motion of the magnetization. Finally, we also numerically simulate the wave propagations of some localized semi-rational solutions and RWs.
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Affiliation(s)
- Xiao-Yong Wen
- School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
| | - Xue-Ke Liu
- School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
| | - Yong Chen
- School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
| | - Zhenya Yan
- KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
- School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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6
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Shao C, Yang L, Yan Y, Wu J, Zhu M, Li L. Periodic, n-soliton and variable separation solutions for an extended (3+1)-dimensional KP-Boussinesq equation. Sci Rep 2023; 13:15826. [PMID: 37739979 PMCID: PMC10517173 DOI: 10.1038/s41598-023-42845-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 09/15/2023] [Indexed: 09/24/2023] Open
Abstract
An extended (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation is studied in this paper to construct periodic solution, n-soliton solution and folded localized excitation. Firstly, with the help of the Hirota's bilinear method and ansatz, some periodic solutions have been derived. Secondly, taking Burgers equation as an auxiliary function, we have obtained n-soliton solution and n-shock wave. Lastly, we present a new variable separation method for (3+1)-dimensional and higher dimensional models, and use it to derive localized excitation solutions. To be specific, we have constructed various novel structures and discussed the interaction dynamics of folded solitary waves. Compared with the other methods, the variable separation solutions obtained in this paper not only directly give the analytical form of the solution u instead of its potential [Formula: see text], but also provide us a straightforward approach to construct localized excitation for higher order dimensional nonlinear partial differential equation.
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Affiliation(s)
- Chuanlin Shao
- School of Economics and Finance, Huaqiao University, Quanzhou, 362021, Fujian, People's Republic of China
| | - Lu Yang
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China
| | - Yongsheng Yan
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China
| | - Jingyu Wu
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China
| | - Minting Zhu
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China
| | - Lingfei Li
- School of Economics and Management, Northwest University, Xi'an, 710127, Shaanxi, People's Republic of China.
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7
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Durairaj P, Kanagaraj S, Kumarasamy S, Rajagopal K. Emergence of extreme events in a quasiperiodic oscillator. Phys Rev E 2023; 107:L022201. [PMID: 36932627 DOI: 10.1103/physreve.107.l022201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2022] [Accepted: 01/23/2023] [Indexed: 06/18/2023]
Abstract
Extreme events are unusual and rare large-amplitude fluctuations can occur unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize extreme events. Different mechanisms for the generation of extreme events and their prediction measures have been reported in the literature. Based on the properties of extreme events, such as those that are rare in the frequency of occurrence and extreme in amplitude, various studies have shown that extreme events are both linear and nonlinear in nature. Interestingly, in this Letter, we report on a special class of extreme events which are nonchaotic and nonperiodic. These nonchaotic extreme events appear in between the quasiperiodic and chaotic dynamics of the system. We report the existence of such extreme events with various statistical measures and characterization techniques.
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Affiliation(s)
- Premraj Durairaj
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600 069, Tamilnadu, India
| | - Sathiyadevi Kanagaraj
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600 069, Tamilnadu, India
| | - Suresh Kumarasamy
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600 069, Tamilnadu, India
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600 069, Tamilnadu, India
- Department of Electronics and Communications Engineering, University Centre for Research and Development, Chandigarh University, Mohali 140 413, Punjab, India
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8
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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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9
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Gorce JB, Falcon E. Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence. PHYSICAL REVIEW LETTERS 2022; 129:054501. [PMID: 35960568 DOI: 10.1103/physrevlett.129.054501] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 04/27/2022] [Accepted: 06/29/2022] [Indexed: 06/15/2023]
Abstract
We investigate experimentally three-dimensional (3D) hydrodynamic turbulence at scales larger than the forcing scale. We manage to perform a scale separation between the forcing scale and the container size by injecting energy into the fluid using centimetric magnetic particles. We measure the statistics of the fluid velocity field at scales larger than the forcing scale (energy spectra, velocity distributions, and energy flux spectrum). In particular, we show that the large-scale dynamics are in statistical equilibrium and can be described with an effective temperature, although not isolated from the turbulent Kolmogorov cascade. In the large-scale domain, the energy flux is zero on average but exhibits intense temporal fluctuations. Our Letter paves the way to use equilibrium statistical mechanics to describe the large-scale properties of 3D turbulent flows.
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Affiliation(s)
- Jean-Baptiste Gorce
- Université Paris Cité, CNRS, MSC Laboratory, UMR 7057, F-75013 Paris, France
| | - Eric Falcon
- Université Paris Cité, CNRS, MSC Laboratory, UMR 7057, F-75013 Paris, France
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10
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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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11
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Weng W, Zhang G, Yan Z. Strong and weak interactions of rational vector rogue waves and solitons to any
n
-component nonlinear Schrödinger system with higher-order effects. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2021.0670] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The higher-order effects play an important role in the wave propagations of ultrashort (e.g. subpicosecond or femtosecond) light pulses in optical fibres. In this paper, we investigate any
n
-component fourth-order nonlinear Schrödinger (
n
-FONLS) system with non-zero backgrounds containing the
n
-Hirota equation and the
n
-Lakshmanan–Porsezian–Daniel equation. Based on the loop group theory, we find the multi-parameter family of novel rational vector rogue waves (RVRWs) of the
n
-FONLS equation starting from the plane-wave solutions. Moreover, we exhibit the weak and strong interactions of some representative RVRW structures. In particular, we also find that the W-shaped rational vector dark and bright solitons of the
n
-FONLS equation as the second- and fourth-order dispersion coefficients satisfy some relation. Furthermore, we find the higher-order RVRWs of the
n
-FONLS equation. These obtained rational solutions will be useful in the study of RVRW phenomena of multi-component nonlinear wave models in nonlinear optics, deep ocean and Bose–Einstein condensates.
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Affiliation(s)
- Weifang Weng
- Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, 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
| | - Guoqiang Zhang
- Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
| | - Zhenya Yan
- Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, 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
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12
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Ablowitz MJ, Cole JT. Transverse Instability of Rogue Waves. PHYSICAL REVIEW LETTERS 2021; 127:104101. [PMID: 34533341 DOI: 10.1103/physrevlett.127.104101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schrödinger equation is often used to model rogue waves; it is an envelope description of plane waves and admits the so-called Pergerine and Kuznetov-Ma soliton solutions. However, in deep water waves and certain electromagnetic systems where there are two significant transverse dimensions, the 2+1 hyperbolic nonlinear Schrödinger equation is the appropriate wave envelope description. Here we show that these rogue wave solutions suffer from strong transverse instability at long and short frequencies. Moreover, the stability of the Peregrine soliton is found to coincide with that of the background plane wave. These results indicate that, when applicable, transverse dimensions must be taken into account when investigating rogue wave pheneomena.
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Affiliation(s)
- Mark J Ablowitz
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
| | - Justin T Cole
- Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80918, USA
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13
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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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14
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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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15
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Zhang G, Ling L, Yan Z, Konotop VV. Parity-time-symmetric rational vector rogue waves of the n-component nonlinear Schrödinger equation. CHAOS (WOODBURY, N.Y.) 2021; 31:063120. [PMID: 34241286 DOI: 10.1063/5.0048922] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 05/31/2021] [Indexed: 06/13/2023]
Abstract
Extreme events are investigated in the integrable n-component nonlinear Schrödinger (NLS) equation with focusing nonlinearity. We report novel multi-parametric families of rational vector rogue wave (RW) solutions featuring the parity-time ( PT) symmetry, which are characterized by non-identical boundary conditions for the components that are consistent with the degeneracy of n branches of Benjamin-Feir instability. Explicit examples of PT-symmetric rational vector RWs are presented. Subject to the specific choice of the parameters, high-amplitude RWs are generated. The effect of a small non-integrable deformation of the 3-NLS equation on the excitation of vector RWs is discussed. The reported results can be useful for the design of experiments for observation of high-amplitude RWs in multi-component nonlinear physical systems.
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Affiliation(s)
- Guoqiang Zhang
- Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
| | - Liming Ling
- School of Mathematics, South China University of Technology, Guangzhou 510640, China
| | - Zhenya Yan
- Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
| | - Vladimir V Konotop
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa 1749-016, Portugal
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16
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Bonatto C, Prado SD, Metz FL, Schoffen JR, Correia RRB, Hickmann JM. Super rogue wave generation in the linear regime. Phys Rev E 2020; 102:052219. [PMID: 33327069 DOI: 10.1103/physreve.102.052219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2019] [Accepted: 11/08/2020] [Indexed: 06/12/2023]
Abstract
Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate super rogue waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of ordinary rogue waves. Here we show, experimentally and theoretically, that optical super rogue waves emerge in the simple case of linear light diffraction in one transverse dimension. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate super rogue events (non-Gaussian statistics with superlong tails). Our results consist in a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.
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Affiliation(s)
- Cristian Bonatto
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Sandra D Prado
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Fernando L Metz
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
- Departamento de Física, Universidade Federal de Santa Maria, 97105-900 Santa Maria, Brazil
- London Mathematical Laboratory, 14 Buckingham Street, London WC2N 6DF, United Kingdom
| | - Júlio R Schoffen
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Ricardo R B Correia
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
| | - Jandir M Hickmann
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil
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17
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Falcon E, Michel G, Prabhudesai G, Cazaubiel A, Berhanu M, Mordant N, Aumaître S, Bonnefoy F. Saturation of the Inverse Cascade in Surface Gravity-Wave Turbulence. PHYSICAL REVIEW LETTERS 2020; 125:134501. [PMID: 33034484 DOI: 10.1103/physrevlett.125.134501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
We report on the observation of surface gravity-wave turbulence at scales larger than the forcing ones in a large basin. In addition to the downscale transfer usually reported in gravity-wave turbulence, an upscale transfer is observed, interpreted as the inverse cascade of weak turbulence theory. A steady state is achieved when the inverse cascade reaches a scale in between the forcing wavelength and the basin size, but far from the latter. This inverse cascade saturation, which depends on the wave steepness, is probably due to the emergence of nonlinear dissipative structures such as sharp-crested waves.
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Affiliation(s)
- E Falcon
- Université de Paris, Univ Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
| | - G Michel
- Sorbonne Université, IJLRA, UMR 7190 CNRS, F-75 005 Paris, France
| | - G Prabhudesai
- Ecole Normale Supérieure, LPS, UMR 8550 CNRS, F-75 205 Paris, France
| | - A Cazaubiel
- Université de Paris, Univ Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
| | - M Berhanu
- Université de Paris, Univ Paris Diderot, MSC, UMR 7057 CNRS, F-75 013 Paris, France
| | - N Mordant
- Université Grenoble Alpes, LEGI, UMR 5519 CNRS, F-38 000 Grenoble, France
| | - S Aumaître
- CEA-Saclay, Sphynx, DSM, URA 2464 CNRS, F-91 191 Gif-sur-Yvette, France
| | - F Bonnefoy
- Ecole Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France
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18
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Kengne E, Liu W. Engineering rogue waves with quintic nonlinearity and nonlinear dispersion effects in a modified Nogochi nonlinear electric transmission network. Phys Rev E 2020; 102:012203. [PMID: 32795018 DOI: 10.1103/physreve.102.012203] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Accepted: 06/12/2020] [Indexed: 11/07/2022]
Abstract
A one-dimensional modified Nogochi nonlinear electric transmission network with dispersive elements that consist of a large number of identical sections is theoretically studied in the present paper. The first-order nonautonomous rogue waves with quintic nonlinearity and nonlinear dispersion effects in this network are predicted and analyzed using the cubic-quintic nonlinear Schrödinger (CQ-NLS) equation with a cubic nonlinear derivative term. The results show that, in the semidiscrete limit, the voltage for the transmission network is described in some cases by the CQ-NLS equation with a derivative term that is derived employing the reductive perturbation technique. A one-parameter first-order rational solution of the derived CQ-NLS equation is presented and used to investigate analytically the dependency of the characteristics of the first-order rouge wave parameters on the electric transmission network under consideration. Our results show that when we change the quintic nonlinear and nonlinear dispersion parameter, the first-order nonautonomous rogue wave transforms into the bright-like soliton. Our results also reveal that the shape of the first-order nonautonomous rogue waves does not change when we tune the quintic nonlinear and nonlinear dispersion parameter, while the quintic nonlinear term and nonlinear dispersion effect affect the velocity of first-rogue waves and the evolution of their phase. We also show that the network parameters as well as the frequency of the carrier voltage signal can be used to manage the motion of the first-order nonautonomous rogue waves in the electrical network under consideration. Our results may help to control and manage rogue waves experimentally in electric networks.
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Affiliation(s)
- Emmanuel Kengne
- School of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua 321004, China
| | - WuMing 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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19
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Tsai JY, Lin PC, I L. Single to multiple acoustic vortex excitations in the transition to defect-mediated dust acoustic wave turbulence. Phys Rev E 2020; 101:023210. [PMID: 32168674 DOI: 10.1103/physreve.101.023210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Accepted: 01/31/2020] [Indexed: 11/07/2022]
Abstract
We experimentally investigate the cooperative excitations in the transition from a self-excited three-dimensional ordered plane wave to a defect-mediated turbulence (DMT) state with multiple unstable defect filaments in a dusty plasma system. It is found that, with increasing effective driving, a single acoustic vortex (AV) with positive or negative helicity winding around a long straight defect filament with small wiggling in the 2+1D (dimensional) space-time space starts to emerge along the center axis of the small dust cluster. The sequential ruptures of the crest surfaces from the cluster boundary followed by their reconnection with adjacent ruptured crest surfaces, or repelling one of the pairwise generated defects out of the boundary, are the key for the single AV generation. Further increasing driving makes the single defect filament exhibit helical excursion in the 2+1D space. The system eventually enters the state with a few short-lived AVs and the DMT state with multiple AVs. The gradual increasing defect filament fluctuations and defect number in the transition to the DMT more strongly distort the nearby waveforms, which leads to the transition from the emergence of distinct sideband peaks to the broadened peaks in the power spectra of temporal dust density fluctuation. For the system with a larger cluster size, the single AV states are skipped in the transition to the DMT state.
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Affiliation(s)
- Jun-Yi Tsai
- Department of Physics and Center for Complex Systems, National Central University, Jhongli, Taiwan 32001, Republic of China.,Molecular Science and Technology, Taiwan International Graduate Program, Academia Sinica and National Central University, Taipei, Taiwan 10617, Republic of China
| | - Po-Cheng Lin
- Department of Physics and Center for Complex Systems, National Central University, Jhongli, Taiwan 32001, Republic of China
| | - Lin I
- Department of Physics and Center for Complex Systems, National Central University, Jhongli, Taiwan 32001, Republic of China
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20
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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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21
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Karachalios NI, Kyriazopoulos P, Vetas K. Excitation of Peregrine-Type Waveforms from Vanishing Initial Conditions in the Presence of Periodic Forcing. ACTA ACUST UNITED AC 2019. [DOI: 10.1515/zna-2018-0540] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Abstract
We show by direct numerical simulations that spatiotemporally localised waveforms, strongly reminiscent of the Peregrine rogue wave, can be excited by vanishing initial conditions for the periodically driven nonlinear Schrödinger equation. The emergence of the Peregrine-type waveforms can be potentially justified, in terms of the existence and modulational instability of spatially homogeneous solutions of the model and the continuous dependence of the localised initial data for small time intervals. We also comment on the persistence of the above dynamics, under the presence of small damping effects, and justify that this behaviour should be considered as far from approximations of the corresponding integrable limit.
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Affiliation(s)
- Nikos I. Karachalios
- Department of Mathematics , University of the Aegean , Karlovassi, GR 83200 Samos , Greece
| | - Paris Kyriazopoulos
- Department of Mathematics , University of the Aegean , Karlovassi, GR 83200 Samos , Greece
| | - Konstantinos Vetas
- Department of Mathematics , University of the Aegean , Karlovassi, GR 83200 Samos , Greece
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22
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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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23
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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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24
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Chowdhury NA, Mannan A, Hasan MM, Mamun AA. Heavy ion-acoustic rogue waves in electron-positron multi-ion plasmas. CHAOS (WOODBURY, N.Y.) 2017; 27:093105. [PMID: 28964149 DOI: 10.1063/1.4985113] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The nonlinear propagation of heavy-ion-acoustic (HIA) waves (HIAWs) in a four-component multi-ion plasma (containing inertial heavy negative ions and light positive ions, as well as inertialess nonextensive electrons and positrons) has been theoretically investigated. The nonlinear Schrödinger (NLS) equation is derived by employing the reductive perturbation method. It is found that the NLS equation leads to the modulational instability (MI) of HIAWs, and to the formation of HIA rogue waves (HIARWs), which are due to the effects of nonlinearity and dispersion in the propagation of HIAWs. The conditions for the MI of HIAWs and the basic properties of the generated HIARWs are identified. It is observed that the striking features (viz., instability criteria, growth rate of MI, amplitude and width of HIARWs, etc.) of the HIAWs are significantly modified by the effects of nonextensivity of electrons and positrons, the ratio of light positive ion mass to heavy negative ion mass, the ratio of electron number density to light positive ion number density, the ratio of electron temperature to positron temperature, etc. The relevancy of our present investigation to the observations in space (viz., cometary comae and earth's ionosphere) and laboratory (viz., solid-high intense laser plasma interaction experiments) plasmas is pointed out.
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Affiliation(s)
- N A Chowdhury
- Department of Physics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh
| | - A Mannan
- Department of Physics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh
| | - M M Hasan
- Department of Physics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh
| | - A A Mamun
- Department of Physics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh
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25
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Rao J, Porsezian K, He J. Semi-rational solutions of the third-type Davey-Stewartson equation. CHAOS (WOODBURY, N.Y.) 2017; 27:083115. [PMID: 28863505 DOI: 10.1063/1.4999083] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators, semi-rational solutions consisting of rogue waves, breathers, and solitons are generated. These semi-rational solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general rogue wave solutions expressed in terms of rational functions. It is shown that the fundamental (simplest) rogue waves are line rogue waves. It is also shown that the multi-rogue waves describe interactions of several fundamental rogue waves, which would generate interesting curvy wave patterns. The higher order rogue waves originate from a localized lump and retreat back to it. Several types of hybrid solutions composed of rogue waves, breathers, and solitons have also been illustrated. Specifically, these semi-rational solutions have a new phenomenon: lumps form on dark solitons and gradual separation from the dark solitons is observed.
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Affiliation(s)
- Jiguang Rao
- Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
| | | | - Jingsong He
- Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
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26
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Kimmoun O, Hsu HC, Kibler B, Chabchoub A. Nonconservative higher-order hydrodynamic modulation instability. Phys Rev E 2017; 96:022219. [PMID: 28950632 DOI: 10.1103/physreve.96.022219] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Indexed: 06/07/2023]
Abstract
The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy sidebands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary sidebands generate an infinite number of additional sidebands, forming a triangular sideband cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive sideband pair that is created is also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirms observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counterintuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids, and plasma.
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Affiliation(s)
- O Kimmoun
- Aix-Marseille University, CNRS, Centrale Marseille, IRPHE, Marseille, France
| | - H C Hsu
- Department of Marine Environment and Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan
| | - B Kibler
- Laboratoire Interdisciplinaire Carnot de Bourgogne-UMR 6303 CNRS/Université Bourgogne Franche-Comté, 21078 Dijon, France
| | - A Chabchoub
- Department of Mechanical Engineering, Aalto University, 02150 Espoo, Finland
- School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
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27
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Ginzburg NS, Rozental RM, Sergeev AS, Fedotov AE, Zotova IV, Tarakanov VP. Generation of Rogue Waves in Gyrotrons Operating in the Regime of Developed Turbulence. PHYSICAL REVIEW LETTERS 2017; 119:034801. [PMID: 28777618 DOI: 10.1103/physrevlett.119.034801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2017] [Indexed: 06/07/2023]
Abstract
Within the framework of the average approach and direct 3D PIC (particle-in-cell) simulations, we demonstrate that the gyrotrons operating in the regime of developed turbulence can sporadically emit "giant" spikes with intensities a factor of 100-150 greater than the average radiation power and a factor of 6-9 exceeding the power of the driving electron beams. Together with the statistical features such as a long-tail probability distribution, this allows the interpretation of generated spikes as microwave rogue waves. The mechanism of spikes formation is related to the simultaneous cyclotron interaction of a gyrating electron beam with forward and backward waves near the waveguide cutoff frequency as well as with the longitudinal deceleration of electrons.
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Affiliation(s)
- N S Ginzburg
- Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
| | - R M Rozental
- Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
| | - A S Sergeev
- Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
| | - A E Fedotov
- Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
| | - I V Zotova
- Institute of Applied Physics, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
| | - V P Tarakanov
- Moscow Engineering Physics Institute, 115409, Moscow, Russia
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28
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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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29
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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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30
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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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31
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El-Labany S, El-Shewy E, Abd El-Razek H, El-Rahman A. Wave propagation in strongly dispersive superthermal dusty plasma. ADVANCES IN SPACE RESEARCH 2017; 59:1962-1968. [DOI: 10.1016/j.asr.2017.01.042] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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32
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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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33
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Emergence of a turbulent cascade in a quantum gas. Nature 2016; 539:72-75. [DOI: 10.1038/nature20114] [Citation(s) in RCA: 124] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2016] [Accepted: 09/10/2016] [Indexed: 11/08/2022]
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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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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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36
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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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37
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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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Choi D, Wishon MJ, Barnoud J, Chang CY, Bouazizi Y, Locquet A, Citrin DS. Low-frequency fluctuations in an external-cavity laser leading to extreme events. Phys Rev E 2016; 93:042216. [PMID: 27176302 DOI: 10.1103/physreve.93.042216] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Indexed: 06/05/2023]
Abstract
We experimentally investigate the dynamical regimes of a laser diode subject to external optical feedback in light of extreme-event (EE) analysis. We observe EEs in the low-frequency fluctuations (LFFs) regime. This number decreases to negligible values when the laser transitions towards fully developed coherence collapse as the injection current is increased. Moreover, we show that EEs observed in the LFF regime are linked to high-frequency pulsing events observed after a power dropout. Finally, we prove experimentally that the observation of EEs in the LFF regimes is robust to changes in operational parameters.
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Affiliation(s)
- Daeyoung Choi
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - Michael J Wishon
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - J Barnoud
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - C Y Chang
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
| | - Y Bouazizi
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - A Locquet
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
| | - D S Citrin
- UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi F-57070, Metz, France
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
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Zhong WP, Belić M, Malomed BA. Rogue waves in a two-component Manakov system with variable coefficients and an external potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:053201. [PMID: 26651808 DOI: 10.1103/physreve.92.053201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2014] [Indexed: 06/05/2023]
Abstract
We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system may be realized in nonlinear optics and Bose-Einstein condensates. By means of a similarity transformation, we establish a connection between solutions of the coupled Manakov system with spatially variable coefficients and the basic Manakov model with constant coefficients. Exact solutions in the form of two-component Peregrine and dromion waves are obtained. The RW dynamics is analyzed for different choices of parameters in the underlying parameter space. Different classes of RW solutions are categorized by means of a naturally introduced control parameter which takes integer values.
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Affiliation(s)
- Wei-Ping Zhong
- Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300, China
- Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar
| | - Milivoj Belić
- Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
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40
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Temgoua DDE, Kofane TC. Nonparaxial rogue waves in optical Kerr media. Phys Rev E 2015; 91:063201. [PMID: 26172812 DOI: 10.1103/physreve.91.063201] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Indexed: 11/07/2022]
Abstract
We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.
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Affiliation(s)
- D D Estelle Temgoua
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
| | - T C Kofane
- Laboratory of Mechanics, Department of Physics, Faculty of Science, 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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41
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Zhong WP, Belić M, Zhang Y. Second-order rogue wave breathers in the nonlinear Schrödinger equation with quadratic potential modulated by a spatially-varying diffraction coefficient. OPTICS EXPRESS 2015; 23:3708-3716. [PMID: 25836223 DOI: 10.1364/oe.23.003708] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Nonlinear Schrödinger equation with simple quadratic potential modulated by a spatially-varying diffraction coefficient is investigated theoretically. Second-order rogue wave breather solutions of the model are constructed by using the similarity transformation. A modal quantum number is introduced, useful for classifying and controlling the solutions. From the solutions obtained, the behavior of second order Kuznetsov-Ma breathers (KMBs), Akhmediev breathers (ABs), and Peregrine solitons is analyzed in particular, by selecting different modulation frequencies and quantum modal parameter. We show how to generate interesting second order breathers and related hybrid rogue waves. The emergence of true rogue waves - single giant waves that are generated in the interaction of KMBs, ABs, and Peregrine solitons - is explicitly displayed in our analytical solutions.
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42
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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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43
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Seshasayanan K, Benavides SJ, Alexakis A. On the edge of an inverse cascade. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:051003. [PMID: 25493730 DOI: 10.1103/physreve.90.051003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2014] [Indexed: 06/04/2023]
Abstract
We demonstrate that systems with a parameter-controlled inverse cascade can exhibit critical behavior for which at the critical value of the control parameter the inverse cascade stops. In the vicinity of such a critical point, standard phenomenological estimates for the energy balance will fail since the energy flux towards large length scales becomes zero. We demonstrate this using the computationally tractable model of two-dimensional (2D) magnetohydrodynamics in a periodic box. In the absence of any external magnetic forcing, the system reduces to hydrodynamic fluid turbulence with an inverse energy cascade. In the presence of strong magnetic forcing, the system behaves as 2D magnetohydrodynamic turbulence with forward energy cascade. As the amplitude of the magnetic forcing is varied, a critical value is met for which the energy flux towards the large scales becomes zero. Close to this point, the energy flux scales as a power law with the departure from the critical point and the normalized amplitude of the fluctuations diverges. Similar behavior is observed for the flux of the square vector potential for which no inverse flux is observed for weak magnetic forcing, while a finite inverse flux is observed for magnetic forcing above the critical point. We conjecture that this behavior is generic for systems of variable inverse cascade.
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Affiliation(s)
- Kannabiran Seshasayanan
- Laboratoire de Physique Statistique, CNRS UMR 8550, École Normale Supérieure, Paris, France, and CNRS, Université Pierre et Marié Curie, Paris, France
| | | | - Alexandros Alexakis
- Laboratoire de Physique Statistique, CNRS UMR 8550, École Normale Supérieure, Paris, France, and CNRS, Université Pierre et Marié Curie, Paris, France and Université Paris Diderot, Paris 75013, France
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44
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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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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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47
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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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Abstract
Wave turbulence (WT) occurs in systems of strongly interacting nonlinear waves and can lead to energy flows across length and frequency scales much like those that are well known in vortex turbulence. Typically, the energy passes although a nondissipative inertial range until it reaches a small enough scale that viscosity becomes important and terminates the cascade by dissipating the energy as heat. Wave turbulence in quantum fluids is of particular interest, partly because revealing experiments can be performed on a laboratory scale, and partly because WT among the Kelvin waves on quantized vortices is believed to play a crucial role in the final stages of the decay of (vortex) quantum turbulence. In this short review, we provide a perspective on recent work on WT in quantum fluids, setting it in context and discussing the outlook for the next few years. We outline the theory, review briefly the experiments carried out to date using liquid H2 and liquid (4)He, and discuss some nonequilibrium excitonic superfluids in which WT has been predicted but not yet observed experimentally. By way of conclusion, we consider the medium- and longer-term outlook for the field.
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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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