Exact solution for (2Â +Â 1)-dimension nonlinear dispersive long wave equation

By using the self-transformation and the homogeneous balance method, we establish the Hopf-Cole transformation which turns the (2 + 1)-dimension nonlinear dispersive long wave equation into the nonlinear heat equation. With it, abundant new exact solutions are obtained, including the multi-solitary wave solution and the rational series solutions, etc. In addition, the new trigonometric function periodic solutions are obtained by using the generalized tanh method.