Bifurcations of travelling wave solutions in a class of generalized KdV equation

By using the bifurcation theory of dynamical systems to a generalized KdV equation given by Cooper et al., the existence of solitary wave solutions, solitary cusp 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. Some exact explicit parametric representations of the above waves are determined.