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The exact traveling wave solutions and their bifurcations in the Gardner and Gardner-KP equations. (English) Zbl 1258.34010

Summary: By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner-KP equation are obtained via an auxiliary function method.

MSC:

34A05 Explicit solutions, first integrals of ordinary differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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