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Related papers: Universal patterns of rogue waves

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The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse…

Exactly Solvable and Integrable Systems · Physics 2015-06-17 Zhenya Yan , Chaoqing Dai

Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS…

Pattern Formation and Solitons · Physics 2007-05-23 Constance Schober , Alvaro Islas

General high-order rogue waves of the NLS-Boussinesq equation are obtained by the KP-hierarchy reduction theory. These rogue waves are expressed with the determinants, whose entries are all algebraic forms. It is found that the fundamental…

Exactly Solvable and Integrable Systems · Physics 2017-10-25 Xiaoen Zhang , Yong Chen

The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schr\"odinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the…

Fluid Dynamics · Physics 2015-11-03 Y. Charles Li

Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schr\"odinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics and plasmas, exhibits…

Pattern Formation and Solitons · Physics 2016-01-07 H. N. Chan , B. A. Malomed , K. W. Chow , E. Ding

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 Schr\"odinger equation is often used to model rogue waves; it…

Pattern Formation and Solitons · Physics 2021-09-14 Mark J. Ablowitz , Justin T. Cole

In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson,…

Pattern Formation and Solitons · Physics 2019-02-15 C. B. Ward , P. G. Kevrekidis

In this paper, general rogue wave solutions in the massive Thirring (MT) model are derived by using the Kadomtsev-Petviashvili (KP) hierarchy reduction method and these rational solutions are presented explicitly in terms of determinants…

Exactly Solvable and Integrable Systems · Physics 2022-08-09 Junchao Chen , Bo Yang , Bao-Feng Feng

This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions of the coupled nonlinear Schr\"odinger (CNLS) equation in the presence of multiple large internal parameters. We report several new high-order RW…

Exactly Solvable and Integrable Systems · Physics 2026-04-30 Zixuan Deng , Huian Lin , Liming Ling

We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and…

Pattern Formation and Solitons · Physics 2022-12-16 Yan-Hong Qin , Liming Ling , Li-Chen Zhao

This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions for any multi-component nonlinear Schr\"odinger equation (denoted as $n$-NLSE) with multiple internal large parameters and reports some new RW…

Exactly Solvable and Integrable Systems · Physics 2025-02-19 Huian Lin , Liming Ling

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

General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free…

Exactly Solvable and Integrable Systems · Physics 2014-04-14 Gui Mu , Zhenyun Qin , Roger Grimshaw

Over the past decade, the rogue wave debate has stimulated the comparison of predictions and observations among different branches of wave physics, particularly between hydrodynamics and optics, in situations where analogous dynamical…

Optics · Physics 2018-02-28 F. Baronio , B. Frisquet , S. Chen , G. Millot , S. Wabnitz , B. Kibler

In this work, we numerically consider the initial value problem for nonlinear Schr\"odinger (NLS) type models arising in the physics of ultracold boson gases, with generic Gaussian wavepacket initial data. The corresponding Gaussian's width…

Pattern Formation and Solitons · Physics 2016-09-08 E. G. Charalampidis , J. Cuevas-Maraver , D. J. Frantzeskakis , P. G. Kevrekidis

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

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

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 rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5…

Fluid Dynamics · Physics 2017-03-30 A. Slunyaev , E. Pelinovsky , A. Sergeeva , A. Chabchoub , N. Hoffmann , M. Onorato , N. Akhmediev

This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue…

Exactly Solvable and Integrable Systems · Physics 2019-03-18 Bo Yang , Jianke Yang