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 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.