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

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

2008-04-08

arxiv.org/abs/0804.1308v1

Mathematics

Analysis of PDEs

Scientific paper

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 Schr\"odinger 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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