Exact periodic waves and their interactions for the (2+1)-dimensional KdV equation

By means of the singular manifold method we obtain a general solution involving three arbitrary functions for the (2+1)-dimensional KdV equation. Diverse periodic wave solutions may be produced by appropriately selecting these arbitrary functions as the Jacobi elliptic functions. The interaction properties of the periodic waves are investigated numerically and found to be nonelastic. The long wave limit yields some new types of solitary wave solutions. Especially the dromion and the solitoff solutions obtained in this paper possess new types of solution structures which are quite different from the basic dromion and solitoff ones reported previously in the literature.