The general peakon-antipeakon solution for the Camassa-Holm equation

Abstract

We compute explicitly the peakon-antipeakon solution of the Camassa-Holm equation $u_t-u_{txx}+3u{u}_x-2u_x{u}_{xx}-u{u}_{xxx}=0$ in the non-symmetric and $\alpha$-dissipative case. The solution experiences wave breaking in finite time, and the explicit solution illuminates the interplay between the various variables.

23 pages, 5 figures

Cited by in corpus (8)

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• Solutions of the Camassa-Holm equation with accumulating breaking times
• A numerical study of variational discretizations of the Camassa-Holm equation
• Uniqueness of dissipative solutions for the Camassa-Holm equation
• Ghostpeakons and Characteristic Curves for the Camassa-Holm, Degasperis-Procesi and Novikov Equations
• Uniqueness of Dissipative Solution for Camassa-Holm Equation with Peakon-Antipeakon Initial Data
• Geometric aspects of two- and threepeakons
• A Lipschitz metric for the Camassa--Holm equation