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We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…

Exactly Solvable and Integrable Systems · Physics 2013-01-08 Nikolay K. Vitanov , Amin Chabchoub , Norbert Hoffmann

We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationaly unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped…

Fluid Dynamics · Physics 2014-07-30 A. Toffoli , T. Waseda , H. Houtani , T. Kinoshita , K. Collins , D. Proment , M. Onorato

An inhomogeneous nonlinear Schr\"odinger equation is considered, that is invariant under $L^2$ scaling. The sharp condition for global existence of $H^1$ solutions is established, involving the $L^2$ norm of the ground state of the…

Analysis of PDEs · Mathematics 2012-11-21 François Genoud

A nonlinear Schr\"odinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of…

Fluid Dynamics · Physics 2015-06-05 Roland Thomas , Christian Kharif , Miguel Manna

We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the standard NLS…

Chaotic Dynamics · Physics 2013-05-15 Miguel Onorato , Davide Proment

We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…

Pattern Formation and Solitons · Physics 2014-10-23 J. S. He , E. G. Charalampidis , P. G. Kevrekidis , D. J. Frantzeskakis

A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…

Pattern Formation and Solitons · Physics 2013-11-28 R. K. Jackson , R. Marangell , H. Susanto

In this letter,the designable integrability(DI) of the variable coefficient derivative nonlinear Schr\"odinger equation (VCDNLSE) is shown by construction of an explicit transformation which maps VCDNLSE to the usual derivative nonlinear…

Exactly Solvable and Integrable Systems · Physics 2012-02-07 Shuwei Xu , Jingsong He , Lihong Wang

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

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

The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the…

Pattern Formation and Solitons · Physics 2017-04-26 Theodoros P. Horikis , Mark J. Ablowitz

The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…

Exactly Solvable and Integrable Systems · Physics 2021-06-09 Jinbing Chen , Dmitry E. Pelinovsky

We present exact solutions for rogue waves arising on the background of periodic waves in the focusing nonlinear Schrodinger equation. The exact solutions are obtained by characterizing the Lax spectrum related to the periodic waves and by…

Exactly Solvable and Integrable Systems · Physics 2020-01-06 Jinbing Chen , Dmitry E. Pelinovsky , Robert E. White

For the one dimensional nonlinear Schr\"odinger equation with triple power nonlinearity and general exponents, we study analytically and numerically the existence and stability of standing waves. Special attention is paid to the curves of…

Analysis of PDEs · Mathematics 2025-08-28 Theo Morrison , Tai-Peng Tsai

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

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

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

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

We predict the existence of linear discrete rogue waves governed by the discrete nonlinear Schrodinger equation. We discuss that Josephson effect is the underlying reason for the formation of such waves.

Optics · Physics 2020-01-08 C. Yuce

Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These…

Exactly Solvable and Integrable Systems · Physics 2018-11-14 Bo Yang , Jianke Yang
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