A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrdinger system  

作　　者：蔡加祥 王雨顺 

机构地区：[1]Jiangsu Key Laboratory for NSLSCS,School of Mathematics Science,Nanjing Normal University [2]School of Mathematics Science,Huaiyin Normal University

出　　处：《Chinese Physics B》2013年第6期135-140,共6页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 11201169 and 11271195);the National Basic Research Program of China (Grant No. 2010AA012304);the Natural Science Foundation of Jiangsu Education Bureau,China (Grant Nos. 10KJB110001 and 12KJB110002);the Qing Lan Project of Jiangsu Province of China

摘　　要：We derive a new method for a coupled nonlinear Schr/Sdinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove the proposed method preserves the charge and energy conservation laws exactly. In numerical tests, we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions. Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws. These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.We derive a new method for a coupled nonlinear Schr/Sdinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove the proposed method preserves the charge and energy conservation laws exactly. In numerical tests, we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions. Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws. These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.

关 键 词：Schroedinger equation Fourier pseudospectral method conservation law energy 

分 类 号：O175.2[理学—数学]