EXISTENCE AND UNIQUENESS OF PERIODIC WAVES FOR A PERTURBED SEXTIC GENERALIZED BBM EQUATION

This paper is devoted to the existence and uniqueness of periodic waves for a perturbed sextic generalized BBM equation with weak backward diffusion and dissipation effects. By applying geometric singular perturbation theory and analyzing the perturbations of a Hamiltonian system with a hyper -elliptic Hamiltonian of degree seven, we prove the existence and uniqueness of periodic wave solutions with each wave speed in an open interval. It is also proved that the periodic wave solution persists for any energy parameter h in an open interval and sufficiently small perturbation parameter. Furthermore, we prove that the wave speed c0(h) is strictly monotonically increasing with respect to h by analyzing Abelian integral having three generating elements. Moreover, the upper and lower bounds of the limiting wave speed are obtained.