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Toffoli A, Alberello A, Clarke H, Nelli F, Benetazzo A, Bergamasco F, Ntamba BN, Vichi M, Onorato M. Observations of Rogue Seas in the Southern Ocean. PHYSICAL REVIEW LETTERS 2024; 132:154101. [PMID: 38682971 DOI: 10.1103/physrevlett.132.154101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2023] [Revised: 01/16/2024] [Accepted: 02/29/2024] [Indexed: 05/01/2024]
Abstract
We report direct observations of surface waves from a stereo camera system along with concurrent measurements of wind speed during an expedition across the Southern Ocean in the austral winter aboard the South African icebreaker S.A. Agulhas II. Records include water surface elevation across a range of wave conditions spanning from early stages of wave growth to full development. We give experimental evidence of rogue seas, i.e., sea states characterized by heavy tails of the probability density function well beyond the expectation based on bound mode theory. These conditions emerge during wave growth, where strong wind forcing and high nonlinearity drive wave dynamics. Quasiresonance wave-wave interactions, which are known to sustain the generation of large amplitude rogue waves, capture this behavior. Wave statistics return to normality as the wind forcing ceases and waves switch to a full developed condition.
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Affiliation(s)
- A Toffoli
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - A Alberello
- School of Mathematics, University of East Anglia, Norwich, United Kingdom
| | - H Clarke
- Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - F Nelli
- Department of Mechnaical Engineering, Swinburne University of Technology, Melbourne, Australia
| | - A Benetazzo
- Istituto di Scienze Marine, Consiglio Nazionale delle Ricerche, 30122 Venice, Italy
| | | | - B Ntamba Ntamba
- Cape Peninsula University of Technology, 7535 Cape Town, South Africa
| | - M Vichi
- Department of Oceanography, University of Cape Town, Cape Town, South Africa
- Marine and Antarctic Research Centre for Innovation and Sustainability, University of Cape Town, Cape Town, South Africa
| | - 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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2
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Pal TK, Ray A, Nag Chowdhury S, Ghosh D. Extreme rotational events in a forced-damped nonlinear pendulum. CHAOS (WOODBURY, N.Y.) 2023; 33:2895983. [PMID: 37307164 DOI: 10.1063/5.0152699] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 05/11/2023] [Indexed: 06/14/2023]
Abstract
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under various interests. This well-deserved focus aids in comprehending various oscillatory physical phenomena that can be reduced to the equations of the pendulum. The present article focuses on the rotational dynamics of the two-dimensional forced-damped pendulum under the influence of the ac and dc torque. Interestingly, we are able to detect a range of the pendulum's length for which the angular velocity exhibits a few intermittent extreme rotational events that deviate significantly from a certain well-defined threshold. The statistics of the return intervals between these extreme rotational events are supported by our data to be spread exponentially at a specific pendulum's length beyond which the external dc and ac torque are no longer sufficient for a full rotation around the pivot. The numerical results show a sudden increase in the size of the chaotic attractor due to interior crisis, which is the source of instability that is responsible for triggering large amplitude events in our system. We also notice the occurrence of phase slips with the appearance of extreme rotational events when the phase difference between the instantaneous phase of the system and the externally applied ac torque is observed.
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Affiliation(s)
- Tapas Kumar Pal
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Arnob Ray
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, California 95616, USA
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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3
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Three-dimensional imaging of waves and floes in the marginal ice zone during a cyclone. Nat Commun 2022; 13:4590. [PMID: 35933464 PMCID: PMC9356999 DOI: 10.1038/s41467-022-32036-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Accepted: 07/12/2022] [Indexed: 11/09/2022] Open
Abstract
The marginal ice zone is the dynamic interface between the open ocean and consolidated inner pack ice. Surface gravity waves regulate marginal ice zone extent and properties, and, hence, atmosphere-ocean fluxes and ice advance/retreat. Over the past decade, seminal experimental campaigns have generated much needed measurements of wave evolution in the marginal ice zone, which, notwithstanding the prominent knowledge gaps that remain, are underpinning major advances in understanding the region's role in the climate system. Here, we report three-dimensional imaging of waves from a moving vessel and simultaneous imaging of floe sizes, with the potential to enhance the marginal ice zone database substantially. The images give the direction-frequency wave spectrum, which we combine with concurrent measurements of wind speeds and reanalysis products to reveal the complex multi-component wind-plus-swell nature of a cyclone-driven wave field, and quantify evolution of large-amplitude waves in sea ice.
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4
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Novkoski F, Falcon E, Pham CT. Experimental Dispersion Relation of Surface Waves along a Torus of Fluid. PHYSICAL REVIEW LETTERS 2021; 127:144504. [PMID: 34652193 DOI: 10.1103/physrevlett.127.144504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2021] [Accepted: 08/16/2021] [Indexed: 06/13/2023]
Abstract
We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatiotemporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous, and sloshing modes. Standing azimuthal waves are also studied leading to polygonlike patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.
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Affiliation(s)
- Filip Novkoski
- Université de Paris, MSC, UMR 7057 CNRS, F-75013 Paris, France
| | - Eric Falcon
- Université de Paris, MSC, UMR 7057 CNRS, F-75013 Paris, France
| | - Chi-Tuong Pham
- Université Paris-Saclay, LISN, UMR 9015 CNRS, F-91405 Orsay, France
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5
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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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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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7
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Fadaeiazar E, Leontini J, Onorato M, Waseda T, Alberello A, Toffoli A. Fourier amplitude distribution and intermittency in mechanically generated surface gravity waves. Phys Rev E 2020; 102:013106. [PMID: 32794909 DOI: 10.1103/physreve.102.013106] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2020] [Accepted: 06/28/2020] [Indexed: 11/07/2022]
Abstract
We examine and discuss the spatial evolution of the statistical properties of mechanically generated surface gravity wave fields, initialized with unidirectional spectral energy distributions, uniformly distributed phases, and Rayleigh distributed amplitudes. We demonstrate that nonlinear interactions produce an energy cascade towards high frequency modes with a directional spread and trigger localized intermittent bursts. By analyzing the probability density function of Fourier mode amplitudes in the high frequency range of the wave energy spectrum, we show that a heavy-tailed distribution emerges with distance from the wave generator as a result of these intermittent bursts, departing from the originally imposed Rayleigh distribution, even under relatively weak nonlinear conditions.
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Affiliation(s)
- Elmira Fadaeiazar
- Department of Mechanical and Product Design Engineering, Swinburne University of Technology, 3122 Hawthorn, Victoria, Australia
| | - Justin Leontini
- Department of Mechanical and Product Design Engineering, Swinburne University of Technology, 3122 Hawthorn, Victoria, Australia
| | - Miguel Onorato
- Dipartimento di Fisica, Universitá di Torino, 10125 Torino, Italy and INFN, 10125 Torino, Italy
| | - Takuji Waseda
- Department of Ocean Technology, Policy and Environment, Graduate School of Frontier Sciences, The University of Tokyo, Tokyo, Japan
| | - Alberto Alberello
- Dipartimento di Fisica, Universitá di Torino, 10125 Torino, Italy and School of Mathematical Sciences, University of Adelaide, 5005 Adelaide, South Australia, Australia
| | - Alessandro Toffoli
- Department of Infrastructure Engineering, The University of Melbourne, 3010 Parkville, Victoria, Australia
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8
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Abstract
The formation of rogue oceanic waves may be the result of different causes. Various factors (winds, currents, dispersive focussing, depth, nonlinear focussing and instability) make this subject intriguing, and yet its understanding is quite relevant to practical issues. Here, we deal only with the nonlinear character of this dynamics, which has been recognised as the main ingredient to rogue wave formation. In this perspective, the formation of rogue waves requires a non-vanishing and unstable background such as a nonlinear regular wave train with attractive self-interaction. The simplest, best known model of such dynamics is the universal nonlinear Schrödinger equation. This has proven to serve as a good approximation in various contexts and over a broad range of experimental settings. This model aims to give the slow evolution of the envelope of one monochromatic wave due to nonlinearity. Here, we naturally consider the same problem for the envelopes of two weakly resonant monochromatic waves. As for the nonlinear Schrödinger equation, which is integrable, we adopt an integrable model to describe the interaction of two waves. This is the system of two coupled nonlinear Schrödinger equations (Manakov model) with self- and cross-interactions that may be both defocussing and focussing. We first discuss the linear stability properties of the background by computing the spectrum for all values of the parameters such as coupling constants and amplitudes. In particular, we relate the instability bands to properties of the spectrum and compute the gain function (or growth rate). We also relate to the stability spectrum the value of the spectral variable, which corresponds to a rogue wave solution. In contrast with the nonlinear Schrödinger equation, different types of single rogue wave exist that correspond to different values of the spectral variable even in the same spectrum. For these critical values, which are completely classified, we give the corresponding explicit expression of the rogue wave solution that follows from the well known Darboux–Dressing transformation method. Although not all systems of two coupled nonlinear Schrödinger equations that have been derived in water wave dynamics are integrable, our investigation contributes to the understanding of new effects due to wave coupling, at least for model equations that, even if not integrable, are close enough to the model considered here. For instance, our findings lead to investigate rogue waves generated by instabilities due to self- and cross-interactions of defocusing type. An illustrative selection of two coupled rogue waves solutions is displayed.
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9
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Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media. APPLIED SCIENCES-BASEL 2018. [DOI: 10.3390/app8122559] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We study the dynamics of a partially incoherent optical pulse that propagates in a slowly responding nonlinear Kerr medium. We show that irrespective of the sign of the dispersion (either normal or anomalous), the incoherent pulse as a whole exhibits a global collective behavior characterized by a dramatic narrowing and amplification in the strongly non-linear regime. The theoretical analysis based on the Vlasov formalism and the method of the characteristics applied to a reduced hydrodynamic model reveal that such a strong amplitude-incoherent pulse originates in the existence of a concurrent shock-collapse singularity (CSCS): The envelope of the intensity of the random wave exhibits a collapse singularity, while the momentum exhibits a shock singularity. The dynamic behavior of the system after the shock-collapse singularity is characterized through the analysis of the phase-space dynamics.
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10
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Zhang Y, Qiu D, Mihalache D, He J. The loop rogue wave solutions for the Wadati-Konno-Ichikawa equation. CHAOS (WOODBURY, N.Y.) 2018; 28:103108. [PMID: 30384668 DOI: 10.1063/1.5053612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2018] [Accepted: 09/20/2018] [Indexed: 06/08/2023]
Abstract
The first-order rogue wave solution with two arbitrary parameters of the Wadati-Konno-Ichikawa equation is generated based on the Darboux transformation and inverse hodograph transformation. The analyticity of first-order rogue wave solution is studied. A simple analysis shows that the parameter that denotes the amplitude of background wave plays an important role in controlling the analyticity of rogue wave solution. In particular, the rogue wave solution displays a loop-type profile when it is singular, and the general features of loop rogue waves are discussed in detail.
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Affiliation(s)
- Yongshuai Zhang
- School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, People's Republic of China
| | - Deqin Qiu
- School of Science, China University of Mining and Technology, Beijing 100083, People's Republic of China
| | - Dumitru Mihalache
- Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, Magurele, RO 077125, Romania
| | - Jingsong He
- Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
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11
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Chen S, Ye Y, Soto-Crespo JM, Grelu P, Baronio F. Peregrine Solitons Beyond the Threefold Limit and Their Two-Soliton Interactions. PHYSICAL REVIEW LETTERS 2018; 121:104101. [PMID: 30240257 DOI: 10.1103/physrevlett.121.104101] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2018] [Indexed: 06/08/2023]
Abstract
Within the coupled Fokas-Lenells equations framework, we show explicitly that, in contrast to the expected threefold-amplitude magnification, Peregrine solitons can reach a peak amplitude as high as 5 times the background level. Besides, the interaction of two such anomalous Peregrine solitons can generate a spikelike rogue wave of extremely high peak amplitude, depending on the parameters used. We numerically confirm that the Peregrine soliton beyond the threefold limit can be reproduced from either a deterministic initial profile or a chaotic background field, hence anticipating the feasibility of its experimental observation.
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Affiliation(s)
- Shihua Chen
- School of Physics, Southeast University, Nanjing 211189, China
| | - Yanlin Ye
- School of Physics, Southeast University, Nanjing 211189, China
| | - Jose M Soto-Crespo
- Instituto de Óptica, Consejo Superior de Investigaciones Científicas (CSIC), Serrano 121, Madrid 28006, Spain
| | - Philippe Grelu
- Laboratoire ICB, U.M.R. 6303 C.N.R.S., Université Bourgogne Franche-Comté, 9 avenue A. Savary, F-21078 Dijon, France
| | - Fabio Baronio
- INO CNR and DII, Università di Brescia, Via Branze 38, 25123 Brescia, Italy
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12
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Hu X, Cubaud T. Viscous Wave Breaking and Ligament Formation in Microfluidic Systems. PHYSICAL REVIEW LETTERS 2018; 121:044502. [PMID: 30095958 DOI: 10.1103/physrevlett.121.044502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Revised: 06/13/2018] [Indexed: 06/08/2023]
Abstract
Rapid layering of viscous materials in microsystems encompasses a range of hydrodynamic instabilities that facilitate mixing and emulsification processes of fluids having large differences in viscosity. We experimentally study the stability of high-viscosity stratifications made of miscible and immiscible fluid pairs in square microchannels and characterize the propagation dynamics of interfacial waves, including breaking and viscous ligament entrainment from wave crests at moderate Reynolds numbers. For large viscosity contrasts, parallel fluid streams adopt widely different velocities and provide a simple model system to probe the role of inflectional instabilities of stratified microflows in relation with classic inviscid-stability theory. We reveal novel viscous wave regimes and unravel dispersion relationships in the presence and absence of interfacial tension. Detailed examination of wave celerity shows the existence of optimal operation conditions for passively disturbing miscible fluid flows and continuously dispersing low-and high-viscosity fluids at the small scale.
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Affiliation(s)
- Xiaoyi Hu
- Department of Mechanical Engineering, Stony Brook University, Stony Brook, New York 11794, USA
| | - Thomas Cubaud
- Department of Mechanical Engineering, Stony Brook University, Stony Brook, New York 11794, USA
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13
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Yang Z, Zhong WP, Belić M, Zhang Y. Controllable optical rogue waves via nonlinearity management. OPTICS EXPRESS 2018; 26:7587-7597. [PMID: 29609312 DOI: 10.1364/oe.26.007587] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Accepted: 02/28/2018] [Indexed: 06/08/2023]
Abstract
Using a similarity transformation, we obtain analytical solutions to a class of nonlinear Schrödinger (NLS) equations with variable coefficients in inhomogeneous Kerr media, which are related to the optical rogue waves of the standard NLS equation. We discuss the dynamics of such optical rogue waves via nonlinearity management, i.e., by selecting the appropriate nonlinearity coefficients and integration constants, and presenting the solutions. In addition, we investigate higher-order rogue waves by suitably adjusting the nonlinearity coefficient and the rogue wave parameters, which could help in realizing complex but controllable optical rogue waves in properly engineered fibers and other photonic materials.
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Armaroli A, Brunetti M, Kasparian J. Recurrence in the high-order nonlinear Schrödinger equation: A low-dimensional analysis. Phys Rev E 2017; 96:012222. [PMID: 29347121 DOI: 10.1103/physreve.96.012222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2017] [Indexed: 06/07/2023]
Abstract
We study a three-wave truncation of the high-order nonlinear Schrödinger equation for deep-water waves (also named Dysthe equation). We validate the model by comparing it to numerical simulation; we distinguish the impact of the different fourth-order terms and classify the solutions according to their topology. This allows us to properly define the temporary spectral upshift occurring in the nonlinear stage of Benjamin-Feir instability and provides a tool for studying further generalizations of this model.
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Affiliation(s)
- Andrea Armaroli
- GAP-Nonlinear, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland and ISE, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
| | - Maura Brunetti
- GAP-Nonlinear, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland and ISE, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
| | - Jérôme Kasparian
- GAP-Nonlinear, Université de Genève, Chemin de Pinchat 22, 1227 Carouge, Switzerland and ISE, Université de Genève, Boulevard Carl-Vogt 66, 1205 Genève, Switzerland
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