IUMJ

Title: Transverse instability for periodic waves of KP-I and Schroedinger equations

Authors: Zevdzhan Hakkaev, Milena Stanislavova and Atanas Stefanov

Issue: Volume 61 (2012), Issue 2, 461-492

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 traveling waves (with period $K$) in the form $u(t,x,y) = \varphi(x-c t)$ 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 $nK$, $n = 2,3,\dots$ or bounded perturbations.