Existence of periodic waves for a perturbed quintic BBM equation
Lina Guo, Yulin Zhao
Abstract
<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ c_0(h) $\end{document}</tex-math></inline-formula> is decreasing on <inline-formula><tex-math id="M2">\begin{document}$ h $\end{document}</tex-math></inline-formula> by analyzing the ratio of Abelian integrals, where <inline-formula><tex-math id="M3">\begin{document}$ h $\end{document}</tex-math></inline-formula> is the energy level value. Moreover, the upper and lower bounds of the limit wave speed are given.