Multi-symplectic method for the generalized (2+1)-dimensional KdV-mKdV equation

In the present paper, a general solution involving three arbitrary functions for the generalized (2+1)-dimensional KdV-mKdV equation, which is derived from the generalized (1+1)-dimensional KdV-mKdV equation, is first introduced by means of the Wiess, Tabor, Carnevale (WTC) truncation method. And then multisymplectic formulations with several conservation laws taken into account are presented for the generalized (2+1)-dimensional KdV-mKdV equation based on the multisymplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from the general solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent to the Preissmann scheme. From the results of the numerical experiments, we can conclude that the multi-symplectic schemes can accurately simulate the periodic wave solutions of the generalized (2+1)-dimensional KdV-mKdV equation while preserve approximately the conservation laws.