Existence of periodic waves for a perturbed quintic BBM equation

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 \begin{document}$ c_0(h) $\end{document} is decreasing on \begin{document}$ h $\end{document} by analyzing the ratio of Abelian integrals, where \begin{document}$ h $\end{document} is the energy level value. Moreover, the upper and lower bounds of the limit wave speed are given.