English
Related papers

Related papers: Rogue waves in nonlocal media

200 papers

Rogue waves, and their periodic counterparts, have been shown to exist in a number of integrable models. However, relatively little is known about the existence of these objects in models where an exact formula is unattainable. In this…

Pattern Formation and Solitons · Physics 2017-12-12 C. B. Ward , P. G. Kevrekidis , N. Whitaker

We investigate rogue wave formation and spectral downshifting in the higher-order nonlinear Schr\"odinger (HONLS) equation and its dissipative extensions: the nonlinear mean-flow damping model (NLD-HONLS) and the viscous damping model…

Pattern Formation and Solitons · Physics 2025-10-31 C. M. Schober , A. Islas

We review recent progress in modeling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation…

Chaotic Dynamics · Physics 2012-07-11 L. H. Ying , Z. Zhuang , E. J. Heller , L. Kaplan

The cubic nonlinear Schrodinger equation (NLS) in one dimension is considered in the presence of an intensity-dependent dispersion term. We study bright solitary waves with smooth profiles which extend from the limit where the dependence of…

Pattern Formation and Solitons · Physics 2024-08-22 P. G. Kevrekidis , D. E. Pelinovsky , R. M. Ross

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on…

Fluid Dynamics · Physics 2007-08-01 V. P. Ruban

We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the…

Dynamical Systems · Mathematics 2022-06-28 William Anderson , Mohammad Farazmand

In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle…

Analysis of PDEs · Mathematics 2026-04-13 Jaime Angulo Pava , Alexander Muñoz

The formation of coherent structures in noise driven phenomena and in Turbulence is a complex and fundamental question. A particulary important structure is the so-called Rogue Wave (RW) that arises as the sudden appearance of a localized…

We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schr\"{o}dinger equation with third-order dispersion. This conceptually novel generation mechanism is based on…

There is considerable fundamental theoretical and applicative interest in obtaining two-dimensional rogue wave similar to one-dimensional rogue wave of the nonlinear Schr\"odinger equation. Here, we first time proposes a self-mapping…

Pattern Formation and Solitons · Physics 2024-02-20 Jie-Fang Zhang , Zhao Zhang , Meng-yang Zhang , Mei-zhen Jin

By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then a general form of nonlocal nonlinear Schrodinger (NNLS) equation with shifted parity, charge-conjugate and delayed time…

Exactly Solvable and Integrable Systems · Physics 2019-03-05 Xi-Zhong Liu

We perform a numerical study of the initial-boundary value problem, with vanishing boundary conditions, of a driven nonlinear Schr\"odinger equation (NLS) with linear damping and a Gaussian driver. We identify Peregrine-like rogue…

Pattern Formation and Solitons · Physics 2019-10-17 G. Fotopoulos , D. J. Frantzeskakis , N. I. Karachalios , P. G. Kevrekidis , V. Koukouloyannis , K. Vetas

Nonlinear excitations of nuclear density are considered in the framework of semiclassical nonlinear nuclear hydrodynamics. Possible types of stationary nonlinear waves in nuclear media are analysed using Nonlinear Schroedinger equation of…

Nuclear Theory · Physics 2009-10-31 V. G. Kartavenko , A. Sandulescu , W. Greiner

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

The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient…

Disordered Systems and Neural Networks · Physics 2019-07-19 G. P. Tsironis , N. Lazarides , A Maluckov , Lj. Hadzievski

On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the…

Pattern Formation and Solitons · Physics 2008-04-24 Maxim A. Molchan

We present determinant expressions for vector rogue wave solutions of the Manakov system, a two-component coupled nonlinear Schr\"odinger equation. As special case, we generate a family of exact and non-symmetric rogue wave solutions of the…

Exactly Solvable and Integrable Systems · Physics 2015-06-22 Jingsong He , Lijuan Guo , Yongshuai Zhang , Amin Chabchoub

We explore rogue wave formation in multimode silicon nitride (Si$_3$N$_4$) waveguides with multimode nonlinear Schr\"odinger equation-based simulations. Pure fundamental-mode excitation produces smooth propagation without extreme events,…

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solutions of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The…

Atmospheric and Oceanic Physics · Physics 2017-03-17 Alexey Slunyaev , Anna Sergeeva , Ira Didenkulova

The issue of a recurrence of the modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation which appears from nowhere (i.e.,…

Fluid Dynamics · Physics 2017-10-05 Alexey Slunyaev , Alexander Dosaev