SYMPLECTIC AND MULTI-SYMPLECTIC SCHEMES FOR THE TWO-DIMENSIONAL NONLINEAR SCHR(o)DINGER EQUATION
二维非线性Schr(o)dinger方程的辛与多辛格式

The two-dimensional nonlinear Schr dinger equation (2D NLSE) with periodic boundary condition is considered in this paper. An implicit symplectic scheme is constructed by using central difference scheme in space and implicit Euler-centered scheme in time. In addition, a midpoint rule multi-symplectic method is obtained by applying a cell vertex finite volume discretization to its multi-symplectic form. Numerical simulations are presented for plane wave solution and singular solution of the 2D NLSE. The results demonstrate the effectiveness of the proposed methods. Furthermore, the two methods are analyzed and compared with each other.