Transverse instability for periodic waves of KP-I and Schr\"odinger 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)=(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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