, Volume 24, Issue 8, pp 1319-1330
Date: 05 Jul 2008

Bifurcations of travelling wave solutions for a two-component camassa-holm equation

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By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed.

The authors are supported by the National Natural Science Foundation of China (10671179) and (10772158)