EXISTENCE AND UNIQUENESS OF PERIODIC WAVES FOR A PERTURBED SEXTIC GENERALIZED BBM EQUATION

Yanfei Dai; Minzhi Wei

doi:10.11948/20220442

2023 Volume 13 Issue 1

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Yanfei Dai, Minzhi Wei. EXISTENCE AND UNIQUENESS OF PERIODIC WAVES FOR A PERTURBED SEXTIC GENERALIZED BBM EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 502-525. doi: 10.11948/20220442

Citation:

Yanfei Dai, Minzhi Wei. EXISTENCE AND UNIQUENESS OF PERIODIC WAVES FOR A PERTURBED SEXTIC GENERALIZED BBM EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 502-525. doi: 10.11948/20220442

EXISTENCE AND UNIQUENESS OF PERIODIC WAVES FOR A PERTURBED SEXTIC GENERALIZED BBM EQUATION

Yanfei Dai^1, ,,
Minzhi Wei²

1.
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China
2.
School of Mathematics and Quantitative Economics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, China

Corresponding author: Email: gnsydyf@126.com (Y. Dai)

Abstract

Abstract

This paper is devoted to the existence and uniqueness of periodic waves for a perturbed sextic generalized BBM equation with weak backward diffusion and dissipation effects. By applying geometric singular perturbation theory and analyzing the perturbations of a Hamiltonian system with a hyper-elliptic Hamiltonian of degree seven, we prove the existence and uniqueness of periodic wave solutions with each wave speed in an open interval. It is also proved that the periodic wave solution persists for any energy parameter $h$ in an open interval and sufficiently small perturbation parameter. Furthermore, we prove that the wave speed $c_0(h)$ is strictly monotonically increasing with respect to $h$ by analyzing Abelian integral having three generating elements. Moreover, the upper and lower bounds of the limiting wave speed are obtained.
- BBM equation /
- hyper-elliptic Hamiltonian system /
- geometric singular perturbation theory /
- periodic waves /
- Abelian integral
MSC: 34C25, 34C60, 37C27

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References

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