Bifurcations of travelling wave solutions in a non-linear dispersive equation

By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin–Bona–Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.