Abstract

Research on traveling wave solutions of generalized Camassa-Holm equation is one of the hottest points in the study of nonlinear dynamic system. The peakon and bifurcations in a generalized Camassa-Holm equation are considered in this paper. By using nonlinear transform and the transform of traveling wave to the generalized Camassa-Holm equation, averaged equation is obtained. We applied the bifurcation theory of planar dynamical system and maple software to investigate the equation. We obtain the peakon from the homoclinic orbit. The results obtained will play an important directive role in the study of Camassa-Holm equation.

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