二维非线性Schrdinger方程的辛与多辛格式  

SYMPLECTIC AND MULTI-SYMPLECTIC SCHEMES FOR THE TWO-DIMENSIONAL NONLINEAR SCHRDINGER EQUATION

作　　者：朱华君[1] 陈亚铭[1] 宋松和[1] 唐贻发[2] 

机构地区：[1]国防科学技术大学数学与系统科学系,长沙410073 [2]中科院数学与系统科学系,北京100080

出　　处：《计算数学》2010年第3期315-326,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10971226);民口973课题(2009CB723802-4)资助项目

摘　　要：对满足周期边界条件的二维非线性Schroedinger方程，运用中心差分对该方程进行空间离散，得到一个有限维Hamilton系统，然后用隐式Euler中点格式进行时间离散得到其辛格式，针对该方程的多辛形式，运用有限体积法离散， 得到一种直平行六面休上的中点型多辛格式．用所构造的辛与多辛格式对二维非线性Schroedinger方程的平面波解和奇异解进行数值模拟，结果验证了所构造格式的有效性．最后，根据计算结果，对两种格式进行，分析和比较．The two-dimensional nonlinear Schroedinger 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.

关 键 词：二维非线性Shroedinger方程 辛格式 有限体积法 多辛格式 

分 类 号：O241.82[理学—计算数学]