中国物理B ›› 1999, Vol. 8 ›› Issue (2): 118-130.doi: 10.1088/1004-423X/8/2/005

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A SOLITON PERTURBATION THEORY FOR THE UNSTABLE NONLINEAR SCHR?DINGER EQUATION WITH CORRECTIONS

黄念宁1, 陈芝得2, 陈向军3   

  1. (1)Department of Physics, Wuhan University, Wuhan 430072, China; (2)Department of Physics, Wuhan University, Wuhan 430072, China; Department of Physics, Guangzhou Normal University, Guangzhou 510400, China; (3)Department of Physics, Wuhan University, Wuhan 430072, China; Department of Physics, Jinan University, Guangzhou 510632, China
  • 收稿日期:1998-07-23 出版日期:1999-02-15 发布日期:1999-02-20

A SOLITON PERTURBATION THEORY FOR THE UNSTABLE NONLINEAR SCHR$\ddot{\rm O}$DINGER EQUATION WITH CORRECTIONS

Chen Zhi-de (陈芝得)ab, Chen Xiang-jun (陈向军)ac, Huang Nian-ning (黄念宁)a   

  1. a Department of Physics, Wuhan University, Wuhan 430072, China; b Department of Physics, Guangzhou Normal University, Guangzhou 510400, China; c Department of Physics, Jinan University, Guangzhou 510632, China
  • Received:1998-07-23 Online:1999-02-15 Published:1999-02-20

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摘要： Based on the Zakharov-Shabat equation of the inverse scattering transform for the unstable nonlinear Schr?dinger equation, for which a perturbation theory with corrections is developed in this paper. All necessary formulae for calculating the scattering data are derived. Based upon these formulae, the effect due to the corrections can be studied. As an example, the correction due to the damping is calculated.

Abstract: Based on the Zakharov-Shabat equation of the inverse scattering transform for the unstable nonlinear Schr$\ddot{\rm o}$dinger equation, for which a perturbation theory with corrections is developed in this paper. All necessary formulae for calculating the scattering data are derived. Based upon these formulae, the effect due to the corrections can be studied. As an example, the correction due to the damping is calculated.

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

  • 03.65.Ge
03.65.Nk (Scattering theory)