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In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal…

Analysis of PDEs · Mathematics 2020-07-28 Boris Buffoni , Mark D. Groves , Shu-Ming Sun , Erik Wahlén

The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA)…

Soft Condensed Matter · Physics 2009-11-10 B. B. Baizakov , B. A. Malomed , M. Salerno

We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong XPM interaction, vector solitons with…

This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under strong surface tension. The waves, constructed via a…

Analysis of PDEs · Mathematics 2025-11-11 Changfeng Gui , Shanfa Lai , Yong Liu , Juncheng Wei , Wen Yang

We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schr\"{o}dinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a…

Analysis of PDEs · Mathematics 2017-12-05 Alex H. Ardila

We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of $N$ incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained…

Pattern Formation and Solitons · Physics 2009-10-31 Dmitry E. Pelinovsky , Yuri S. Kivshar

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the…

Pattern Formation and Solitons · Physics 2012-06-07 F. Maucher , W. Krolikowski , S. Skupin

A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…

Quantum Gases · Physics 2016-12-21 Boris A. Malomed

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4+1) dimensions, and find there are two cases to consider; what we call non-exceptional and exceptional. In…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Sigbjorn Hervik , Hari K. Kunduri , James Lucietti

We study (2+1)-dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents, and demonstrate that these solitary waves exhibit a symmetry-breaking instability provided their total…

Pattern Formation and Solitons · Physics 2009-11-07 Anton S. Desyatnikov , Yuri S. Kivshar , Kristian Motzek , Friedemann Kaiser , Carsten Weilnau , Cornelia Denz

We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov-Kuznetsov equation in dimensions two and three. Moreover, we derive a qualitative version of the orbital stability result which turns out to…

Analysis of PDEs · Mathematics 2025-10-14 Didier Pilod , Frédéric Valet

We consider the NLS system of the third-harmonic generation, which was introduced by Sammut. Our interest is in solitary wave solutions and their stability properties. The recent work of Oliveira and Pastor, discussed global well-posedness…

Analysis of PDEs · Mathematics 2023-04-05 Abba Ramadan , Atanas G. Stefanov

We study the bound states of two-dimensional bright solitons in nonlocal nonlinear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady…

Pattern Formation and Solitons · Physics 2009-11-11 V. M. Lashkin , A. I. Yakimenko , O. O. Prikhodko

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…

Analysis of PDEs · Mathematics 2019-02-07 Swann Marx , Yacine Chitour , Christophe Prieur

In this work, we present a stability criteria for the solitary wave solutions to a BBM system that contains coupled nonlinear terms. Using the idea by Bona, Chen and Karakashian and exploiting the accurate point spectrum information of the…

Analysis of PDEs · Mathematics 2015-05-29 Hongqiu Chen , Xiaojun Wang

It is shown that the interaction of a plasma with thermal radiation leads to the stabilization of both periodic and solitary nonlinear plasma waves. The stabilized periodic nonlinear plasma waves were indeed observed in the experiment…

Plasma Physics · Physics 2007-05-23 Fedor V. Prigara

This paper proves existence and stability results of solitary-wave solutions to coupled nonlinear Schr\"{o}dinger equations with power-type nonlinearities arising in several models of modern physics. The existence of solitary waves is…

Analysis of PDEs · Mathematics 2015-08-11 Santosh Bhattarai

We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution…

Pattern Formation and Solitons · Physics 2012-05-15 Gennadiy Burlak , Boris A. Malomed

This paper sheds new light on the stability properties of solitary wave solutions associated with models of Korteweg-de Vries and Benjamin\&Bona\&Mahoney type, when the dispersion is very lower. Via an approach of compactness, analyticity…

Analysis of PDEs · Mathematics 2018-03-14 Jaime Angulo Pava

The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis…

Pattern Formation and Solitons · Physics 2016-10-12 Theodoros P. Horikis