Symbolic computation and new families of exact travelling solutions for the Kawahara and modified Kawahara equations

In this paper, we consider the nonlinear evolution equations such as Kawahara equation and modified Kawahara equation. By using the tanh method and an exp-function method, the travelling wave solutions for the these equations are presented. New exact travelling solutions are explicitly obtained with the aid of symbolic computation. The obtained solutions include compactons, solitons, solitary patterns and periodic solutions.