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

作者：Minakov Alexander^*

来源：Journal of Differential Equations, 2016, 261(11): 6055-6098.

DOI：10.1016/j.jde.2016.08.028

• Camassa-Holm equation
• Riemann-Hilbert problem
• Step-like initial data
• g-Function approach

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 modulated finite-gap elliptic function and a finite number of solitons.

• 出版日期2016-12-5