中国物理B ›› 2007, Vol. 16 ›› Issue (9): 2503-2509.doi: 10.1088/1009-1963/16/9/003

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Asymptotical solutions of coupled nonlinear Schr?dinger equations with perturbations

叶丽军1, 程雪苹2, 林机2   

  1. (1)Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; (2)Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China;The Abdus Salam International Center for Theoretical Physics, Trieste 34139, Italy
  • 收稿日期:2006-08-30 修回日期:2007-02-03 出版日期:2007-09-20 发布日期:2007-09-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10575087) and the Natural Science Foundation of Zhejiang Province of China (Grant No 102053).

Asymptotical solutions of coupled nonlinear Schrödinger equations with perturbations

Cheng Xue-Ping(程雪苹)a)b), Lin Ji(林机)a)b)†, and Ye Li-Jun(叶丽军)a)   

  1. a Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; b The Abdus Salam International Center for Theoretical Physics, Trieste 34139, Italy
  • Received:2006-08-30 Revised:2007-02-03 Online:2007-09-20 Published:2007-09-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10575087) and the Natural Science Foundation of Zhejiang Province of China (Grant No 102053).

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摘要： In this paper Lou's direct perturbation method is applied to the perturbed coupled nonlinear Schr\"{odinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear Schr\"{odinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.

关键词: direct perturbation method, perturbed coupled nonlinear Schr\"{odinger equations, solitons, asymptotical solutions

Abstract: In this paper Lou's direct perturbation method is applied to the perturbed coupled nonlinear Schrödinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear Schrödinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.

Key words: direct perturbation method, perturbed coupled nonlinear Schr?dinger equations, solitons, asymptotical solutions

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

  • 03.65.Ge
02.30.Nw (Fourier analysis) 05.45.Yv (Solitons)