Stability of Line Solitons for the KP-II Equation in $\mathbb{R}^2$
- ISBN-10
- 1470414244
- ISBN-13
- 9781470414245
- Category
- Representations of algebras
- Pages
- 95
- Language
- English
- Published
- 2015-10-27
- Publisher
- American Mathematical Soc.
- Author
- Tetsu Mizumachi
Description
The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as . He finds 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 . 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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