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arXiv · 1605.07554

Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schrödinger equation

J. Escorcia·E. Suazo
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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.

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J. Escorcia, E. Suazo. 2016-05-24. Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schrödinger equation. https://arxiv.org/abs/1605.07554

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