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Related papers: Rogue waves in nonlocal media

200 papers

We study the standing periodic waves in the semi-discrete integrable system modelled by the Ablowitz-Ladik equation. We have related the stability spectrum to the Lax spectrum by separating the variables and by finding the characteristic…

Exactly Solvable and Integrable Systems · Physics 2023-03-31 Jinbing Chen , Dmitry E. Pelinovsky

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

We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…

Pattern Formation and Solitons · Physics 2024-02-21 G. N. Koutsokostas , S. Sypsas , O. Evnin , T. P. Horikis , D. J. Frantzeskakis

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

This paper delves into the study of multi-component derivative nonlinear Schrodinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation (DT) method, we derive higher-order vector rogue wave…

Exactly Solvable and Integrable Systems · Physics 2023-12-20 Lin Huian , Ling Liming

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 generation of Rossby rogue waves (Rossby rogons), as well as the excitation of bright and dark Rossby envelpe solitons are demonstrated on the basis of the modulational instability (MI) of a coherent Rossby wave packet. The evolution of…

Plasma Physics · Physics 2012-12-11 A. P. Misra , P. K. Shukla

In this article, we derive rogue wave (RW) solutions of a fifth-order nonlinear Schr\"odinger equation over a double-periodic wave background. Choosing the elliptic functions (combinations of $cn$, $dn$ and $sn$) as seed solutions in the…

Exactly Solvable and Integrable Systems · Physics 2022-07-28 N. Sinthuja , M. Senthilvelan

In many physical contexts, notably including deep water waves, modulation instability in one space dimension is often studied using the nonlinear Schr\"odinger equation. The principal solutions of interest are solitons and breathers which…

Fluid Dynamics · Physics 2022-06-13 Montri Maleewong , Roger Grimshaw

We perform statistical analysis on discrete nonlinear waves generated though modulational instability in the context of the Salerno model that interpolates between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable discrete…

Pattern Formation and Solitons · Physics 2009-11-13 A. Maluckov , Lj. Hadzievski , N. Lazarides , G. P. Tsironis

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We…

Pattern Formation and Solitons · Physics 2018-09-19 E. G. Charalampidis , J. Lee , P. G. Kevrekidis , C. Chong

We study the evolution of localized wave groups in unidirectional water wave envelope equations (nonlinear Schrodinger (NLS) and modified NLS (MNLS)). These localizations of energy can lead to disastrous extreme responses (rogue waves).…

Pattern Formation and Solitons · Physics 2015-01-22 Will Cousins , Themistoklis P. Sapsis

We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement…

Fluid Dynamics · Physics 2019-12-24 J. M. Dudley , G. Genty , A. Mussot , A. Chabchoub , F. Dias

Breathers and rogue waves of special coupled nonlinear Schr\"odinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence.…

Pattern Formation and Solitons · Physics 2014-10-29 Jin Hua Li , Hiu Ning Chan , Kin Seng Chiang , Kwok Wing Chow

Formation of giant waves in sea states with two spectral maxima, centered at close wave vectors ${\bf k}_0\pm\Delta {\bf k}/2$ in the Fourier plane, is numerically simulated using the fully nonlinear model for long-crested water waves [V.…

Fluid Dynamics · Physics 2015-05-13 V. P. Ruban

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…

A nonlocal derivative NLS (nonlinear Schr\"{o}dinger) equation describes modulations of waves in a stratified fluid and a continuous limit of the Calogero--Moser--Sutherland system of particles. For the defocusing version of this equation,…

Exactly Solvable and Integrable Systems · Physics 2025-01-28 Jinbing Chen , Dmitry E. Pelinovsky

We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schr\"odinger equation (fNLSE). This is done by invoking a…

Pattern Formation and Solitons · Physics 2024-05-21 T. Congy , G. A. El , G. Roberti , A. Tovbis , S. Randoux , P. Suret

The efforts to understand the physics of rogue waves have motivated the study of mechanisms that produce rare, extreme events, often through analogous optical setups. As many studies have reported nonlinear generation mechanisms, recent…

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