The Solutions of the NLS Equations with Self-Consistent Sources

Yijun Shao; Yunbo Zeng

doi:10.1088/0305-4470/38/11/008

The Solutions of the NLS Equations with Self-Consistent Sources

Exactly Solvable and Integrable Systems 2009-11-10 v1

Authors: Yijun Shao , Yunbo Zeng

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Abstract

We construct the generalized Darboux transformation with arbitrary functions in time $t$ for the AKNS equation with self-consistent sources (AKNSESCS) which, in contrast with the Darboux transformation for the AKNS equation, provides a non-auto-B\"{a}cklund transformation between two AKNSESCSs with different degrees of sources. The formula for N-times repeated generalized Darboux transformation is proposed. By reduction the generalized Darboux transformation with arbitrary functions in time $t$ for the Nonlinear Schr\"{o}dinger equation with self-consistent sources (NLSESCS) is obtained and enables us to find the dark soliton, bright soliton and positon solutions for NLS $^{+}$ ESCS and NLS $^{-}$ ESCS. The properties of these solution are analyzed.

Keywords

NLS equation with self-consistent sources Darboux transformation AKNS equation dark soliton bright soliton positon

Cite

@article{arxiv.nlin/0412071,
  title  = {The Solutions of the NLS Equations with Self-Consistent Sources},
  author = {Yijun Shao and Yunbo Zeng},
  journal= {arXiv preprint arXiv:nlin/0412071},
  year   = {2009}
}

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24 pages, 3 figures, to appear in Journal of Physics A: Mathematical and General

The Solutions of the NLS Equations with Self-Consistent Sources

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