中国物理B ›› 2005, Vol. 14 ›› Issue (2): 231-237.doi: 10.1088/1009-1963/14/2/002

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Dynamic properties of the cubic nonlinear Schr?dinger equation by symplectic method

刘学深, 魏佳羽, 丁培柱   

  1. Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China
  • 收稿日期:2004-04-21 修回日期:2004-11-04 出版日期:2005-03-02 发布日期:2005-03-02
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10171039 and 10074019), the Special Foundation for State Major Basic Research Programme of China (Grant No G1999032804) and the Young Teacher Foundation of Jilin University.

Dynamic properties of the cubic nonlinear Schrödinger equation by symplectic method

Liu Xue-Shen (刘学深), Wei Jia-Yu (魏佳羽), Ding Pei-Zhu (丁培柱)   

  1. Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China
  • Received:2004-04-21 Revised:2004-11-04 Online:2005-03-02 Published:2005-03-02
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10171039 and 10074019), the Special Foundation for State Major Basic Research Programme of China (Grant No G1999032804) and the Young Teacher Foundation of Jilin University.

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摘要： The dynamic properties of a cubic nonlinear Schr?dinger equation are investigated numerically by using the symplectic method with different space approximations. The behaviours of the cubic nonlinear Schr?dinger equation are discussed with different cubic nonlinear parameters in the harmonically modulated initial condition. We show that the conserved quantities will be preserved for long-time computation but the system will exhibit different dynamic behaviours in space difference approximation for the strong cubic nonlinearity.

关键词: dynamic property, conserved quantity, symplectic method

Abstract: The dynamic properties of a cubic nonlinear Schr?dinger equation are investigated numerically by using the symplectic method with different space approximations. The behaviours of the cubic nonlinear Schr?dinger equation are discussed with different cubic nonlinear parameters in the harmonically modulated initial condition. We show that the conserved quantities will be preserved for long-time computation but the system will exhibit different dynamic behaviours in space difference approximation for the strong cubic nonlinearity.

Key words: dynamic property, conserved quantity, symplectic method

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge
05.45.-a (Nonlinear dynamics and chaos) 02.60.-x (Numerical approximation and analysis)