Explicit solutions of the Camassa–Holm equation

E.J. Parkes and V.O. Vakhnenko

Chaos, Solitons & Fractals, 2005, vol. 26, issue 5, 1309-1316

Abstract: Explicit travelling-wave solutions of the Camassa–Holm equation are sought. The solutions are characterized by two parameters. For propagation in the positive x-direction, both periodic and solitary smooth-hump, peakon, cuspon and inverted-cuspon waves are found. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. Some composite wave solutions of the Degasperis–Procesi equation are given in an appendix.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:26:y:2005:i:5:p:1309-1316

DOI: 10.1016/j.chaos.2005.03.011

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