# Transverse spectral stability of small periodic traveling waves for the KP equation - Mathematics > Analysis of PDEs

Transverse spectral stability of small periodic traveling waves for the KP equation - Mathematics > Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: The Kadomtsev-Petviashvili KP equation possesses a four-parameter family ofone-dimensional periodic traveling waves. We study the spectral stability ofthe waves with small amplitude with respect to two-dimensional perturbationswhich are either periodic in the direction of propagation, with the same periodas the one-dimensional traveling wave, or non-periodic localized or bounded.We focus on the so-called KP-I equation positive dispersion case, for whichwe show that these periodic waves are unstable with respect to both types ofperturbations. Finally, we briefly discuss the KP-II equation, for which weshow that these periodic waves are spectrally stable with respect toperturbations which are periodic in the direction of propagation, and have longwavelengths in the transverse direction.

Author: ** Mariana Haragus LM-Besançon**

Source: https://arxiv.org/