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

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

paper · doi:10.48550/arxiv.0804.1308

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.

Cited by

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

Related

• Transverse nonlinear instability for two-dimensional dispersive models
• Transverse instability of the CH-KP-I equation
• Transverse nonlinear instability of Euler-Korteweg solitons
• A simple criterion of transverse linear instability for solitary waves
• The Transverse Instability of Periodic Waves in Zakharov-Kuznetsov Type Equations