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General rogue waves in the Davey-Stewartson-I equation are derived by the bilinear method. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then…

Exactly Solvable and Integrable Systems · Physics 2015-06-05 Yasuhiro Ohta , Jianke Yang

The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in a from of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive…

Pattern Formation and Solitons · Physics 2024-05-31 Yuchen He , Jinghua Wang , Bertrand Kibler , Amin Chabchoub

Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…

Fluid Dynamics · Physics 2017-03-17 Victor Shrira , Alexey Slunyaev

Rogue waves are solitary waves with extreme amplitudes, which appear to be a ubiquitous phenomenon in nonlinear wave propagation, with the requirement for a nonlinearity being their only unifying characteristics. While many mechanisms have…

The appearance of rogue waves in deep sea is investigated using the modified nonlinear Schr\"odinger (MNLS) equation in one spatial-dimension with random initial conditions that are assumed to be normally distributed, with a spectrum…

Fluid Dynamics · Physics 2018-01-24 Giovanni Dematteis , Tobias Grafke , Eric Vanden-Eijnden

In the framework of the focusing Nonlinear Schrodinger (NLS) equation we study numerically the nonlinear stage of the modulation instability (MI) of the condensate. As expected, the development of the MI leads to formation of "integrable…

Exactly Solvable and Integrable Systems · Physics 2015-09-15 D. S. Agafontsev , V. E. Zakharov

The rogue waves in a resonant erbium-doped fibre system governed by a coupled system of the nonlinear Schr\"odinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the…

Exactly Solvable and Integrable Systems · Physics 2015-06-11 Jingsong He , Shuwei Xu , K. Porseizan

In this brief report we study numerically the spontaneous emergence of rogue waves in (i) modulationally unstable plane wave at its long-time statistically stationary state and (ii) bound-state multi-soliton solutions representing the…

Pattern Formation and Solitons · Physics 2022-12-09 D. S. Agafontsev , A. A. Gelash

General rogue waves in the focusing and defocusing Ablowitz-Ladik equations are derived by the bilinear method. In the focusing case, it is shown that rogue waves are always bounded. In addition, fundamental rogue waves reach peak…

Exactly Solvable and Integrable Systems · Physics 2015-06-18 Yasuhiro Ohta , Jianke Yang

This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schr\"odinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit…

Analysis of PDEs · Mathematics 2024-08-13 Deniz Bilman , Peter D. Miller

The dynamics of wave groups is studied for long waves, using the framework of the Benjamin-Bona-Mahony (BBM) equation and its generalizations. It is shown that the dynamics are richer than the corresponding results obtained just from the…

Pattern Formation and Solitons · Physics 2025-05-27 Andrei Marin , Adrian Stefan Carstea

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…

Exactly Solvable and Integrable Systems · Physics 2015-03-13 Anjan Kundu , Abhik Mukherjee , Tapan Naskar

We first report the first- and higher-order vector Peregrine solitons (alias rational rogue waves) for the any multi-component NLS equations based on the loop group theory, an explicit (n + 1)-multiple eigenvalue of a characteristic…

Exactly Solvable and Integrable Systems · Physics 2021-11-19 Guoqiang Zhang , Liming Ling , Zhenya Yan

The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr\"odinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained…

Exactly Solvable and Integrable Systems · Physics 2015-05-20 Zhenya Yan

The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction.…

Exactly Solvable and Integrable Systems · Physics 2019-12-04 Junchao Chen , Liangyuan Chen , Bao-Feng Feng , Ken-ichi Maruno

General high-order rogue waves in the nonlinear Schroedinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the…

Exactly Solvable and Integrable Systems · Physics 2015-05-30 Yasuhiro Ohta , Jianke Yang

Some years ago, Chen, Pelinovsky, and White claimed existence of certain solutions of the nonlinear Schr\"odinger equation for modelling rogue waves [arXiv: 1909.08165v1 (2019)]. It is the aim of this Comment to outline that this claim is…

Exactly Solvable and Integrable Systems · Physics 2025-08-05 Hans Werner Schuermann , Valery Serov

Optical rogue waves are demonstrated in the far-field scattered radiation from photonic arrays designed according to the aperiodic distributions of prime elements in complex quadratic fields. Specifically, by studying light diffraction from…

We investigate rogue-wave solutions in a three-component coupled nonlinear Schrodinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a…

Pattern Formation and Solitons · Physics 2015-01-26 Li-Chen Zhao , Jie Liu

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…

Chaotic Dynamics · Physics 2007-05-23 P. K. Shukla , I. Kourakis , B. Eliasson , M. Marklund , L. Stenflo