Travelling wave solutions for a class of the generalized Benjamin–Bona–Mahoney equations

In this paper, a class of the generalized Benjamin–Bona–Mahony (GBBM) equations with negative exponents are investigated by using the theory of bifurcations of dynamical systems. As a result, the dynamical behavior of different physical structure: solitary patterns, solitons, perodic, kink and anti-kink wave solutions are obtained. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given and some exact solutions are shown.