On the Bifurcation of Traveling Wave Solution of Generalized Camassa-Holm Equation
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چکیده
The generalized Camassa-Holm equation ut + 2kux − uxxt + auux = 2uxuxx + uuxxx + γuxxx is considered in this paper. Under traveling wave variable substitution, the equation is related to a planar singular system. By making a transformation this singular system becomes a regular system. Through discussing the dynamical behavior of the regular system, the explicit periodic blow-up solutions and solitary wave solutions of the generalized Camassa-Holm equation are obtained. Also the limit forms of those solutions are presented.
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تاریخ انتشار 2008