By using the bifurcation theory of dynamical systems for the (2+1)-dimensional Perturbed-KdV equation, the existence of solitary wave and periodic cusp wave are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above waves are given. All exact explicit parametric representations of the above waves are determined.

bifurcation theory of dynamical systems, periodic cusp wave, solitary wave, the (2+1)-dimensional Perturbed-KdV equation.