2013/03/14 by Mizumachi, Tetsu · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1303.3532
We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as x→∞. 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=±∞. 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.