Existence of Kink and Antikink Wave Solutions of Singularly Perturbed Modified Gardner Equation

Weifang Yan, Linlin Wang and Min Zhang ()
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Weifang Yan: School of Mathematics and Statistics Science, Ludong University, Yantai 264001, China
Linlin Wang: School of Mathematics and Statistics Science, Ludong University, Yantai 264001, China
Min Zhang: School of Science, Hunan Institution of Technology, Hengyang 421002, China

Mathematics, 2024, vol. 12, issue 6, 1-9

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 perturbation parameter is sufficiently small, we obtain the sufficient conditions to guarantee the existence of kink and antikink wave solutions.

Keywords: modified Gardner equation; kink and antikink waves; geometric singular perturbation theory; Melnikov function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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