中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60207-060207.doi: 10.1088/1674-1056/22/6/060207

• GENERAL • 上一篇    下一篇

A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system

蔡加祥a b, 王雨顺a   

  1. a Jiangsu Key Laboratory for NSLSCS, School of Mathematics Science, Nanjing Normal University, Nanjing 210046, China;
    b School of Mathematics Science, Huaiyin Normal University, Huaian 223300, China
  • 收稿日期:2012-10-09 修回日期:2012-12-06 出版日期:2013-05-01 发布日期:2013-05-01
  • 基金资助:
    Project 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), and the Qing Lan Project of Jiangsu Province of China.

A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system

Cai Jia-Xiang (蔡加祥)a b, Wang Yu-Shun (王雨顺)a   

  1. a Jiangsu Key Laboratory for NSLSCS, School of Mathematics Science, Nanjing Normal University, Nanjing 210046, China;
    b School of Mathematics Science, Huaiyin Normal University, Huaian 223300, China
  • Received:2012-10-09 Revised:2012-12-06 Online:2013-05-01 Published:2013-05-01
  • Contact: Wang Yu-Shun E-mail:thomasjeer@sohu.com, wangyushun@njnu.edu.cn
  • Supported by:
    Project 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), and the Qing Lan Project of Jiangsu Province of China.

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摘要： We derive a new method for coupled nonlinear Schrödinger 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 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 solitons collision. 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: Schrö, dinger equation, Fourier pseudospectral method, conservation law, energy

Abstract: We derive a new method for coupled nonlinear Schrödinger 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 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 solitons collision. 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.

Key words: Schrödinger equation, Fourier pseudospectral method, conservation law, energy

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
02.70.Bf (Finite-difference methods) 02.70.Jn (Collocation methods) 02.70.Hm (Spectral methods)