Stability of line solitons for the KP-II equation in ${\mathbb{R}}^2$

Abstract

We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as $x\to \infty$. We find that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward $y=\pm \infty$. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.

76pages, no figure

References in corpus (2)

• Global well-posedness for the KP-I equation on the background of a non localized solution
• Remarks on the mass constraint for KP type equations