Browsing by Author "Chen, XJ"

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A direct theory for the perturbed unstable nonlinear Schrodinger equation
(2000-05-01)
Huang, NN
;
Chi, S
;
Lou, BL
;
Chen, XJ
;
光電工程學系
A direct perturbation theory for the unstable nonlinear Schrodinger equation with perturbations is developed. The linearized operator is derived and the squared Jost functions are shown to be its eigenfunctions. Then the equation of linearized operator is transformed into an equivalent 4x4 matrix form with first order derivative in t and the eigenfunctions into a four-component row. Adjoint functions and the inner product are defined. Orthogonality relations of these functions are derived and the expansion of the unity in terms of the four-component eigenfunctions is implied. The effect of damping is discussed as an example. (C) 2000 American Institute of Physics. [S0022- 2488(00)00405-9].
Foundation of direct perturbation method for dark solitons
(1999-05-28)
Huang, NN
;
Chi, S
;
Chen, XJ
;
光電工程學系
;
Department of Photonics
The foundation of the direct perturbation theory for solitons is a complete set of the squared Jest functions. With a suitable definition of the adjoint functions and inner products which yields orthogonal relations, the expansion of the the unity is obtained and the completeness is shown by a generalized Marchenko equation. The direct perturbation method for dark solitons is generalized to the multi-soliton case.