Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients  

作　　者：廖翠萃 崔金超 梁久祯 丁效华 

机构地区：[1]Department of Inforation and Computing Science,College of Science,Jiangnan University,Wuxi 214122,China [2]College of Internet of Things,Jiangnan University,Wuxi 214122,China [3]Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China

出　　处：《Chinese Physics B》2016年第1期419-427,共9页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11401259);the Fundamental Research Funds for the Central Universities,China(Grant No.JUSRR11407)

摘　　要：In this paper, we propose a variational integrator for nonlinear Schrodinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrodinger equations with variable coefficients, cubic nonlinear Schrodinger equations and Gross-Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.In this paper, we propose a variational integrator for nonlinear Schrodinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrodinger equations with variable coefficients, cubic nonlinear Schrodinger equations and Gross-Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.

关 键 词：multi-symplectic form formulas variational integrators conservation laws nonlinear Schr/Sdingerequations 

分 类 号：O175.29[理学—数学]