Transverse Nonlinear Instability of Solitary Waves for Some Hamiltonian Pde’s Frederic Rousset and Nikolay Tzvetkov
نویسنده
چکیده
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.
منابع مشابه
A Simple Criterion of Transverse Linear Instability for Solitary Waves
We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various examples from mathematical physics.
متن کاملTransverse nonlinear instability for two-dimensional dispersive models
We present a method to prove nonlinear instability of solitary waves in dispersive models. Two examples are analyzed: we prove the nonlinear long time instability of the KdV solitary wave (with respect to periodic transverse perturbations) under a KP-I flow and the transverse nonlinear instability of solitary waves for the cubic nonlinear Schrödinger equation.
متن کاملTransverse Instability of the Line Solitary Water-waves
We prove the linear and nonlinear instability of the line solitary water waves with respect to transverse perturbations.
متن کاملInstability of the KdV soliton under a KP-I flow
We prove the nonlinear long time instability of the KdV solitary wave (with respect to periodic transverse perturbations) under a KP-I flow.
متن کاملDynamics of Three-Dimensional Gravity-Capillary Solitary Waves in Deep Water
A model equation for gravity-capillary waves in deep water is proposed. This model is a quadratic approximation of the deep water potential flow equations and has wavepacket-type solitary wave solutions. The model equation supports line solitary waves which are spatially localized in the direction of propagation and constant in the transverse direction, and lump solitary waves which are spatial...
متن کامل