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.
Received: 04 February 1999
Revised: 03 April 1999
Accepted manuscript online:
Fund: 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.
Cite this article:
CHEN SHI-RONG (陈世荣), CHEN ZHI-DE (陈芝得), YUAN XIAN-ZHANG (袁先漳), HUANG NIAN-NING (黄念宁) A DIRECT PERTURBATION THEORY OF THE NONLINEAR SCHR$\ddot{\rm O}$DINGER EQUATION WITH CORRECTIONS 1999 Acta Physica Sinica (Overseas Edition) 8 590
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