Abstract
In this paper, the peakons and bifurcations in a generalized Camassa-Holm equation are studied by using the bifurcation method and qualitative theory of dynamical systems. First, the averaged equation is obtained by introducing linear transform and traveling wave transform to the generalized Camassa-Holm equation. Then, we applied the bifurcation theory of planar dynamical system and maple software to investigate the averaged equation. The phase portrait of the system under a parameter condition is obtained. Finally, we get the peakons from the limit of general single solitary wave solution.
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