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

Abstract

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.

References in corpus (3)

• An index theorem for the stability of periodic traveling waves of KdV type
• Center stable manifolds for quasilinear parabolic pde and conditional stability of nonclassical viscous shock waves
• Stability of periodic traveling waves for complex modified Korteweg-de Vries equation

Cited by in corpus (1)

• Linear stability analysis for periodic traveling waves of the Boussinesq equation and the KGZ system