Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic NonlinearityReport as inadecuate




Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity - Download this document for free, or read online. Document in PDF available to download.

Advances in Mathematical Physics - Volume 2014 2014, Article ID 323591, 6 pages -

Review Article

Laboratory for Theoretical Physics and Material Physics, Faculty of Sciences, Hassiba Benbouali University of Chlef, BP 151, 02000 Chlef, Algeria

Physics Department, United Arab Emirates University, P.O. Box 15551, Al-Ain, United Arab Emirates

Received 23 March 2014; Revised 25 August 2014; Accepted 28 August 2014; Published 15 September 2014

Academic Editor: Ricardo Weder

Copyright © 2014 H. Chachou Samet et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We derive the solitonic solution of the nonlinear Schrödinger equation with cubic nonlinearity, complex potentials, and time-dependent coefficients using the Darboux transformation. We establish the integrability condition for the most general nonlinear Schrödinger equation with cubic nonlinearity and discuss the effect of the coefficients of the higher-order terms in the solitonic solution. We find that the third-order dispersion term can be used to control the soliton motion without the need for an external potential. We discuss the integrability conditions and find the solitonic solution of some of the well-known nonlinear Schrödinger equations with cubic nonlinearity and time-dependent coefficients. We also investigate the higher-order nonlinear Schrödinger equation with cubic and quintic nonlinearities.





Author: H. Chachou Samet, M. Benarous, M. Asad-uz-zaman, and U. Al Khawaja

Source: https://www.hindawi.com/



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