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Bifurcation of exact traveling wave solutions for Gardner and Gardner-KP equations

Ping Cai, Jia-Shi Tang, Zhen-Bo Li

Abstract



By using the method of dynamical systems, the bifurcation and exact traveling wave solutions of Gardner and Gardner-KP equations are studied. The two nonlinear evolution equations are transformed to the same planar dynamical system through some fractional transformations, and Qualitative analysis are preformed to the system. With the help of the relationship between the traveling wave solutions of the partial differential equation and the orbits of the corresponding ordinary differential equation, all bifurcation of phase portraits under different parameter conditions are obtained. The explicit parameter expressions of all types of bounded traveling wave solutions are given, and some of them are new.

Keywords


Bifurcation, solitary wave solution, kink (anti-kink) wave solution, periodic wave solution.

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