School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
5-28-2016
Abstract
In this work, after reviewing two different ways to solve Riccati systems, we are able to present an extensive list of families of integrable nonlinear Schrödinger (NLS) equations with variable coefficients. Using Riccati equations and similarity transformations, we are able to reduce them to the standard NLS models. Consequently, we can construct bright-, dark- and Peregrine-type soliton solutions for NLS with variable coefficients. As an important application of solutions for the Riccati equation with parameters, by means of computer algebra systems, it is shown that the parameters change the dynamics of the solutions. Finally, we test numerical approximations for the inhomogeneous paraxial wave equation by the Crank-Nicolson scheme with analytical solutions found using Riccati systems. These solutions include oscillating laser beams and Laguerre and Gaussian beams.
Recommended Citation
Amador, Gabriel, Kiara Colon, Nathalie Luna, Gerardo Mercado, Enrique Pereira, and Erwin Suazo. "On solutions for linear and nonlinear Schrödinger equations with variable coefficients: A computational approach." Symmetry 8, no. 6 (2016): 38. https://doi.org/10.3390/sym8060038
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Symmetry
DOI
10.3390/sym8060038
Comments
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).