New peaked solitary wave solutions of the generalized Camassa-Holm equation. (English) Zbl 1068.35123

Summary: We consider generalized Camassa-Holm equations and the generalized weakly dissipative Camassa-Holm equations and derive some new exact peaked solitary wave solutions. For \(m=3\), where \(m\) is a representative of the strength of the nonlinearity, we give two types new exact traveling wave solutions of the generalized weakly dissipative Camassa-Holm equations.


35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
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