On existence of kink and antikink wave solutions of singularly perturbed Gardner equation. (English) Zbl 1455.34047
This paper study the persistence of kink and antikink wave solutions of the singularly perturbed Gardner equation from the geometric perspective. In my opinion, first of all, the topic is important and interesting. Besides, the work is novel compared to [Y. Tang et al., Chaos Solitons Fractals 37, No. 2, 532–538 (2008; Zbl 1143.35359)], which focused on the persistence of the solitary wave solution. What’s more, it is a good try to study the persistence of kink solutions by combining the geometric singular perturbation theory and the Melnikov function method.
Reviewer: Hong Li (Jiujiang)
MSC:
| 34C37 | Homoclinic and heteroclinic solutions to ordinary differential equations |
| 34E15 | Singular perturbations for ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 35B25 | Singular perturbations in context of PDEs |
| 35C07 | Traveling wave solutions |
| 34E10 | Perturbations, asymptotics of solutions to ordinary differential equations |
Keywords:
geometric singular perturbation theory; kink and antikink waves; Melnikov function; singularly perturbed Gardner equationCitations:
Zbl 1143.35359References:
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