On the Application of a Generalized Version of the Dressing Method to the Integration of Variable Coefficient N-Coupled Nonlinear Schrödinger Equation

DOI

10.1142/S1402925112500283How to use a DOI?

Keywords

Variable-coefficient; the generalized dressing method; integrability

Abstract

N-coupled nonlinear Schrödinger (NLS) equations have been proposed to describe N-pulse simultaneous propagation in optical fibers. When the fiber is nonuniform, N-coupled variable-coefficient NLS equations can arise. In this paper, a family of N-coupled integrable variable-coefficient NLS equations are studied by using a generalized version of the dressing method. We first extend the dressing method to the versions with (N + 1) × (N + 1) operators and (2N + 1) × (2N + 1) operators. Then, we obtain three types of N-coupled variable-coefficient equations (N-coupled NLS equations, N-coupled Hirota equations and N-coupled high-order NLS equations). Then, the compatibility conditions are given, which insure that these equations are integrable. Finally, the explicit solutions of the new integrable equations are obtained.

Copyright

© 2012 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Ting Su
AU  - Huihui Dai
AU  - Xian Guo Geng
PY  - 2012
DA  - 2012/12/31
TI  - On the Application of a Generalized Version of the Dressing Method to the Integration of Variable Coefficient N-Coupled Nonlinear Schrödinger Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 458
EP  - 476
VL  - 19
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500283
DO  - 10.1142/S1402925112500283
ID  - Su2012
ER  -