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Tian, Lixin; Yin, Jiuli

New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa–Holm equations. (English) Zbl 1046.35101

Chaos Solitons Fractals 20, No. 2, 289-299 (2004).
Summary: We introduce the fully nonlinear generalized Camassa-Holm equation \(C(m,n,p)\) and by using four direct ansatzes, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations.

Cited in 33 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
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\textit{L. Tian} and \textit{J. Yin}, Chaos Solitons Fractals 20, No. 2, 289--299 (2004; Zbl 1046.35101)
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