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.
Asymptotics of step-like solutions for the Camassa-Holm equation / Minakov, O.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 261:11(2016), pp. 6055-6098. [10.1016/j.jde.2016.08.028]
Asymptotics of step-like solutions for the Camassa-Holm equation
Minakov, O.
2016-01-01
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.| File | Dimensione | Formato | |
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