Exact solitary wave solutions of the nonlinear Schr\"odinger equation with a source

T. Soloman Raju; C. Nagaraja Kumar; Prasanta K. Panigrahi

Exact solitary wave solutions of the nonlinear Schr\"odinger equation with a source

Exactly Solvable and Integrable Systems 2007-05-23 v2

Authors: T. Soloman Raju , C. Nagaraja Kumar , Prasanta K. Panigrahi

Abstract

We use a fractional transformation to connect the traveling wave solutions of the nonlinear Schr\"odinger equation (NLSE), phase-locked with a source, to the elliptic functions satisfying, $f^{\prime\prime}\pm af\pm \lambda f^{3}=0$ . The solutions are {\it necessarily} of the rational form, containing both trigonometric and hyperbolic types as special cases. Bright, and dark solitons, respectively, for attractive and repuslive type of nonlinearities, as also singular solitons, are obtained in suitable range of parameter values.

Keywords

nonlinear schrödinger equation solitary wave solutions fractional transformation elliptic functions bright solitons dark solitons

Cite

@article{arxiv.nlin/0308012,
  title  = {Exact solitary wave solutions of the nonlinear Schr\"odinger equation with a source},
  author = {T. Soloman Raju and C. Nagaraja Kumar and Prasanta K. Panigrahi},
  journal= {arXiv preprint arXiv:nlin/0308012},
  year   = {2007}
}

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Presentation of the paper changed for better clarity of the results. References added

Exact solitary wave solutions of the nonlinear Schr\"odinger equation with a source

Abstract

Keywords

Cite

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