Exact periodic and solitary waves and their interactions for the ( [formula omitted])-dimensional KdV equation

Abstract

A general solution involving three arbitrary functions is first obtained for a ( 2 + 1 )-dimensional KdV equation by means of WTC truncation method. Then exact periodic wave solutions are expressed in terms of rational functions of the Jacobi elliptic functions. Limit cases are studied and some interesting, new solitary structures are revealed. The interaction properties between Jacobi elliptic waves (various limit cases) are investigated numerically. The fusion and fission of y-periodic solitary waves is for the first time reported.