Existence of Kink and Antikink Wave Solutions of Singularly Perturbed Modified Gardner Equation
Weifang Yan,
Linlin Wang,
Min Zhang
Abstract:In this paper, the singularly perturbed modified Gardner equation is considered. Firstly, for the unperturbed equation, under certain parameter conditions, we obtain the exact expressions of kink wave solution and antikink wave solution by using the bifurcation method of dynamical systems. Then, the persistence of the kink and antikink wave solutions of the perturbed modified Gardner equation is studied by exploiting the geometric singular perturbation theory and the Melnikov function method. When the perturba… Show more
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