# Direct perturbation theory for the dark soliton solution to the nonlinear Schroedinger equation with normal dispersion

## Abstract

After finding the basic solutions of the linearized nonlinear Schroedinger equation by the method of separation of variables, the perturbation theory for the dark soliton solution is constructed by linear Green's function theory. In application to the self-induced Raman scattering, the adiabatic corrections to the soliton's parameters are obtained and the remaining correction term is given as a pure integral with respect to the continuous spectral parameter.

- Authors:

- Department of Physics, Wuhan University, Wuhan, 430072 (China)

- Publication Date:

- OSTI Identifier:
- 21072425

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevE.75.046604; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRECTIONS; GREEN FUNCTION; INTEGRALS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PERTURBATION THEORY; RAMAN EFFECT; RAMAN SPECTRA; SCHROEDINGER EQUATION; SOLITONS

### Citation Formats

```
Yu Jialu, Yang Chunnuan, Cai Hao, and Huang Nianning.
```*Direct perturbation theory for the dark soliton solution to the nonlinear Schroedinger equation with normal dispersion*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.046604.

```
Yu Jialu, Yang Chunnuan, Cai Hao, & Huang Nianning.
```*Direct perturbation theory for the dark soliton solution to the nonlinear Schroedinger equation with normal dispersion*. United States. doi:10.1103/PHYSREVE.75.046604.

```
Yu Jialu, Yang Chunnuan, Cai Hao, and Huang Nianning. Sun .
"Direct perturbation theory for the dark soliton solution to the nonlinear Schroedinger equation with normal dispersion". United States.
doi:10.1103/PHYSREVE.75.046604.
```

```
@article{osti_21072425,
```

title = {Direct perturbation theory for the dark soliton solution to the nonlinear Schroedinger equation with normal dispersion},

author = {Yu Jialu and Yang Chunnuan and Cai Hao and Huang Nianning},

abstractNote = {After finding the basic solutions of the linearized nonlinear Schroedinger equation by the method of separation of variables, the perturbation theory for the dark soliton solution is constructed by linear Green's function theory. In application to the self-induced Raman scattering, the adiabatic corrections to the soliton's parameters are obtained and the remaining correction term is given as a pure integral with respect to the continuous spectral parameter.},

doi = {10.1103/PHYSREVE.75.046604},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 4,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}

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