Traveling Wave Solutions for a Coupled KdV Equations

In this paper, we use a method in order to find exact explicit traveling solutions in the subspace of the phase space for coupled KdV equations. The key idea is removing a coupled relation for the given system so that the new systems can be solved. The existence of solitary wave solutions is obtained. It is shown that bifurcation theory of dynamical systems provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics.