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Stability of Line Solitons for the KP-II Equation in R

Posted By: nebulae
Stability of Line Solitons for the KP-II Equation in R

Tetsu Mizumachi, "Stability of Line Solitons for the KP-II Equation in R"
English | ISBN: 1470414244 | 2015 | 95 pages | PDF | 1 MB

The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as y→∞. 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 y=±∞. 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.