Asymptotics of step-like solutions for the Camassa-Holm equation

2015/12/15 by Minakov, Alexander · 1 citation
#35B40 #37K05 #37K10 #37K15 #37K40 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1512.04762

Abstract

We study the long-time asymptotics of solution of the Cauchy problem for the Camassa-Holm equation with a step-like initial datum. By using the nonlinear steepest descent method and the so-called g-function approach, we show that the Camassa-Holm equation exhibits a rich structure of sharply separated regions in the x,t-half-plane with qualitatively different asymptotics, which can be described in terms of a sum of modulated finite-gap hyperelliptic or elliptic functions and a finite number of solitons.

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