Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schr\"{o}dinger equation

J. Escorcia; E. Suazo

Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schr\"{o}dinger equation

Mathematical Physics 2016-05-25 v1 math.MP

Authors: J. Escorcia , E. Suazo

Abstract

In this paper, by means of similarity transformations we study exact analytical solutions for a generalized nonlinear Schr $\ddot{\mbox{o}}$ dinger equation with variable coefficients. This equation appears in literature describing the evolution of coherent light in a nonlinear Kerr medium, Bose-Einstein condensates phenomena and high intensity pulse propagation in optical fibers. By restricting the coefficients to satisfy Ermakov-Riccati systems with multiparameter solutions, we present conditions for existence of explicit solutions with singularities and a family of oscillating periodic soliton-type solutions. Also, we show the existence of bright-, dark- and Peregrine-type soliton solutions, and by means of a computer algebra system we exemplify the nontrivial dynamics of the solitary wave center of these solutions produced by our multiparameter approach.

Keywords

nonlinear Schrödinger equation variable coefficients similarity transformations soliton solutions blow-up Ermakov-Riccati systems Peregrine soliton

Cite

@article{arxiv.1605.07554,
  title  = {Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schr\"{o}dinger equation},
  author = {J. Escorcia and E. Suazo},
  journal= {arXiv preprint arXiv:1605.07554},
  year   = {2016}
}

Comments

27 pages, Soliton-like equations, Nonlinear Schr\"{o}dinger like equations, Fiber optics, Gross-Pitaevskii equation, Similarity transformations and Riccati-Ermakov systems

Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schr\"{o}dinger equation

Abstract

Keywords

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