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arXiv · 1303.3532

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

Tetsu Mizumachi
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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.

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Tetsu Mizumachi. 2013-03-14. Stability of line solitons for the KP-II equation in $\R^2$. https://arxiv.org/abs/1303.3532

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