Smooth and non-smooth traveling wave solutions of a class of nonlinear dispersive equation

Xiaoshan Zhao, Aidi Wu and Wenzhang He

Chaos, Solitons & Fractals, 2009, vol. 41, issue 4, 2168-2177

Abstract: There is the widespread existence of wave phenomena in physics, mechanics. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In this paper, we study a nonlinear dispersive K(n,−n,2n) equation, which can be regarded as a generalized K(n,n) equation. Applying the bifurcation theory and the method of phase portraits analysis, we obtain the dynamical behavior and special exact solutions of the K(n,−n,2n) equation. As a result, the conditions under which peakon and compacton solutions appear are also given and the analytic expressions of peakon solutions, compacton and periodic cusp wave solutions are obtained.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:4:p:2168-2177

DOI: 10.1016/j.chaos.2008.08.014

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