EXISTENCE OF PERIODIC AND KINK WAVES IN A PERTURBED DEFOCUSING MKDV EQUATION

Hong Li; Lilin Ma; Mei Liu

doi:10.11948/20200227

2021 Volume 11 Issue 2

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Hong Li, Lilin Ma, Mei Liu. EXISTENCE OF PERIODIC AND KINK WAVES IN A PERTURBED DEFOCUSING MKDV EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 1029-1038. doi: 10.11948/20200227

Citation:

Hong Li, Lilin Ma, Mei Liu. EXISTENCE OF PERIODIC AND KINK WAVES IN A PERTURBED DEFOCUSING MKDV EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 1029-1038. doi: 10.11948/20200227

EXISTENCE OF PERIODIC AND KINK WAVES IN A PERTURBED DEFOCUSING MKDV EQUATION

1.
Department of Mathematics, Jiujiang University, Jiujiang 332005, China
2.
Information Technology Center, Jiujiang University, Jiujiang 332005, China

Corresponding author: Email: Lchzxz3@126.com(H. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (11861040, 11961037) and Program for Innovation training of Jiangxi Province (S202011843012)

Abstract

Abstract

In this paper, we consider the existence of periodic and kink wave solutions of a perturbed defocusing mKdV equation. Based on geometric singular perturbation theory, Chebyshev criteria and bifurcation theory of dynamic system, the wave speed conditions for the periodic and kink solutions are given. The monotonicity of the wave speed is proved, and moreover the upper and lower bounds of the limiting wave speeds are obtained. The uniqueness of the periodic waves is established by showing that the Abelian integrals form a Chebyshev set. In addition, there is no coexistence of one periodic and one solitary waves. The proof process does not need any explicit expression of the original defocusing mKdV periodic wave or kink wave solutions.
- Defocusing mKdV equation /
- traveling wave /
- Abelian integral /
- Chebyshev system
MSC: 34C60, 37C27, 37C29

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References

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