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

Authors :
Weifang Yan
Linlin Wang
Min Zhang
Source :
Mathematics, Vol 12, Iss 6, p 928 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

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.

Details

Language :
English
ISSN :
22277390
Volume :
12
Issue :
6
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.08b51c037db446839177f78735fa99fd
Document Type :
article
Full Text :
https://doi.org/10.3390/math12060928