Abstract
In this paper, we consider the nonlinear equations such as the generalized Kawahara equation and Modified Kawahara equation. By applied the modified extended direct algebraic (MEDA) method, the traveling wave solutions for these equations are presented. New exact traveling solutions are explicitly obtained with the help of symbolic computation, provides a very effective and powerful (mathematical tools) for discrete nonlinear evolution equations in mathematical physics. The obtained solutions include compactons, solutions, solitary patterns and periodic solutions.