Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's
Résumé
We present a general result of transverse nonlinear instability of Id solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1-d model and the transverse perturbation "have the same sign". Our result applies to the generalized KP-I equation, the Nonlinear Schrodinger equation, the generalized Boussinesq system and the Zakharov-Kuznetsov equation and we hope that it may be useful in other contexts. (C) 2008 Elsevier Masson SAS. All rights reserved.