Existence of periodic waves for a perturbed quintic BBM equation

Lina Guo, ,School of Mathematics(Zhuhai), Sun Yat-Sen university, Zhuhai 519082, China, Yulin Zhao
2020 Discrete and Continuous Dynamical Systems. Series A  
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,
more » ... el value. Moreover, the upper and lower bounds of the limit wave speed are given.
doi:10.3934/dcds.2020198 fatcat:2brc6x63cbcdrfg7l43ky4onxa