Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity
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 a...
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2014-01-01
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Series: | Advances in Mathematical Physics |
Online Access: | http://dx.doi.org/10.1155/2014/323591 |
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doaj-dc78d54ec8404473aa95d7bc7e2f77562021-07-02T02:05:57ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/323591323591Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic NonlinearityH. Chachou Samet0M. Benarous1M. Asad-uz-zaman2U. Al Khawaja3Laboratory for Theoretical Physics and Material Physics, Faculty of Sciences, Hassiba Benbouali University of Chlef, BP 151, 02000 Chlef, AlgeriaLaboratory for Theoretical Physics and Material Physics, Faculty of Sciences, Hassiba Benbouali University of Chlef, BP 151, 02000 Chlef, AlgeriaPhysics Department, United Arab Emirates University, P.O. Box 15551, Al-Ain, United Arab EmiratesPhysics Department, United Arab Emirates University, P.O. Box 15551, Al-Ain, United Arab EmiratesWe 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.http://dx.doi.org/10.1155/2014/323591 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
H. Chachou Samet M. Benarous M. Asad-uz-zaman U. Al Khawaja |
spellingShingle |
H. Chachou Samet M. Benarous M. Asad-uz-zaman U. Al Khawaja Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity Advances in Mathematical Physics |
author_facet |
H. Chachou Samet M. Benarous M. Asad-uz-zaman U. Al Khawaja |
author_sort |
H. Chachou Samet |
title |
Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity |
title_short |
Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity |
title_full |
Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity |
title_fullStr |
Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity |
title_full_unstemmed |
Effect of Third-Order Dispersion on the Solitonic Solutions of the Schrödinger Equations with Cubic Nonlinearity |
title_sort |
effect of third-order dispersion on the solitonic solutions of the schrödinger equations with cubic nonlinearity |
publisher |
Hindawi Limited |
series |
Advances in Mathematical Physics |
issn |
1687-9120 1687-9139 |
publishDate |
2014-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2014/323591 |
work_keys_str_mv |
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