# American Institute of Mathematical Sciences

August  2020, 40(8): 4689-4703. doi: 10.3934/dcds.2020198

## Existence of periodic waves for a perturbed quintic BBM equation

 School of Mathematics(Zhuhai), Sun Yat-Sen university, Zhuhai 519082, China

* Corresponding author: Yulin Zhao

Received  May 2019 Revised  February 2020 Published  May 2020

Fund Project: This research is supported by the NSF of China (No.11971495 and No.11801582)

This paper dealt with the existence of periodic waves for a perturbed quintic BBM equation by using geometric singular perturbation theory. By analyzing the perturbations of the Hamiltonian vector field with a hyperelliptic Hamiltonian of degree six, we proved that periodic wave solutions persist for sufficiently small perturbation parameter. It is also proved that the wave speed $c_0(h)$ is decreasing on $h$ by analyzing the ratio of Abelian integrals, where $h$ is the energy level value. Moreover, the upper and lower bounds of the limit wave speed are given.

Citation: Lina Guo, Yulin Zhao. Existence of periodic waves for a perturbed quintic BBM equation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (8) : 4689-4703. doi: 10.3934/dcds.2020198
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##### References:
The phase portrait of system (1.13)
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