New solitary wave solutions in a perturbed generalized BBM equation

Abstract

In this manuscript, based on the geometric singular perturbation theory, several new solitary wave solutions in a perturbed generalized Benjamin–Bona–Mahony (BBM) equation are detected by the explicit calculation of the associated Melnikov integrals. These solitary wave solutions are homoclinic to non-trivial steady states and have not been found before. We also determine the zeroth-order approximations to the speeds of these solitary waves explicitly. In the calculations of the Melnikov integrals, the explicit expressions of the unperturbed homoclinic orbits play an important role.