THE EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS IN THE GARDNER AND GARDNER–KP EQUATIONS

By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner–KP equation are obtained via an auxiliary function method.