Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's

2008/04/08 by Frederic Rousset, Nikolay Tzvetkov, Rousset, Frederic +1 · 1 citation
Mathematics · #35BXX #35Q55 #37K05 #37L50 #81Q20 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35BXX #msc:35Q55 #msc:37K05 #msc:37L50 #msc:81Q20

paper · pdf · doi:10.48550/arxiv.0804.1308

arxiv created 2008/04/08 · arxiv updated 2016/09/08

Abstract

We present a general result of transverse nonlinear instability of 1-d solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1d model and the transverse perturbation "have the same sign". Our result applies to the generalized KP-I equation, the Nonlinear Schrödinger equation, the generalized Boussinesq system and the Zakharov-Kuznetsov equation and we hope that it may be useful in other contexts.

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• Revisiting the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system

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