中国物理B ›› 1999, Vol. 8 ›› Issue (8): 590-597.doi: 10.1088/1004-423X/8/8/006

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A DIRECT PERTURBATION THEORY OF THE NONLINEAR SCHR?DINGER EQUATION WITH CORRECTIONS

陈芝得1, 陈世荣2, 袁先漳2, 黄念宁2   

  1. (1)Department of Physics, Guangzhou Normal University,Guangzhou 510400,China; (2)Department of Physics, Wuhan University,Wuhan 430072,China
  • 收稿日期:1999-02-04 修回日期:1999-04-03 出版日期:1999-08-15 发布日期:1999-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China(Grant No.19775037) and by the Doctoral Foundation of the State Education Commission of China.

A DIRECT PERTURBATION THEORY OF THE NONLINEAR SCHR$\ddot{\rm O}$DINGER EQUATION WITH CORRECTIONS

CHEN SHI-RONG (陈世荣)a, CHEN ZHI-DE (陈芝得)b, YUAN XIAN-ZHANG (袁先漳)a, 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
  • Received:1999-02-04 Revised:1999-04-03 Online:1999-08-15 Published:1999-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China(Grant No.19775037) and by the Doctoral Foundation of the State Education Commission of China.

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摘要： An exact direct perturbation theory of nonlinear Schrodinger equation with corrections is developed under the condition that the initial value of the perturbed solution is equal to the value of an exact multisoliton solution at a particular time. After showing the squared Jost functions are the eigenfunctions of the linearized operator with a vanishing eigenvalue,suitable definitions of adjoint functions and inner product are introduced. Orthogonal relations are derived and the expansion of the unity in terms of the squared Jost functions is naturally implied. The completeness of the squared Jost functions is shown by the generalized Marchenko equation. As an example,the evolution of a Raman loss compensated soliton in an optical fiber is treated.

Abstract: An exact direct perturbation theory of nonlinear Schrodinger equation with corrections is developed under the condition that the initial value of the perturbed solution is equal to the value of an exact multisoliton solution at a particular time. After showing the squared Jost functions are the eigenfunctions of the linearized operator with a vanishing eigenvalue,suitable definitions of adjoint functions and inner product are introduced. Orthogonal relations are derived and the expansion of the unity in terms of the squared Jost functions is naturally implied. The completeness of the squared Jost functions is shown by the generalized Marchenko equation. As an example,the evolution of a Raman loss compensated soliton in an optical fiber is treated.

中图分类号:  (Solitons)

  • 05.45.Yv
02.60.Lj (Ordinary and partial differential equations; boundary value problems) 42.81.Dp (Propagation, scattering, and losses; solitons) 02.10.Ud (Linear algebra) 02.30.Tb (Operator theory)