Transverse instability for periodic waves of KP-I and Schrödinger equations

Details Transverse instability for periodic waves of KP-I and Schrödinger equations Transverse instability for periodic waves of KP-I and Schrödinger equations

2010-12-14

arxiv.org/abs/1012.3065v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the quadratic and cubic KP - I and NLS models in $1+2$ dimensions with periodic boundary conditions. We show that the spatially periodic travelling waves (with period $K$) in the form $u(t,x,y)=\vp(x-c t)$ are spectrally and linearly unstable, when the perturbations are taken to be with the same period. This strong instability implies other instabilities considered recently - for example with respect to perturbations with periods $nK, n=2, 3, ...$ or bounded perturbations.

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