Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials

Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials

We consider coupled nonlinear Schrodinger equation (CNLSE) of the Gross-Pitaevskii-type, with linear mixing and nonlinear cross-phase modulation. Motivated by the study of matter waves in Bose-Einstein condensates and multicomponent (vectorial) nonlinear optical systems, we investigate the eigenvalu...

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Main Authors: Hamdy I. Abdel-Gawad, A. Biswas, A.S. Alshomrani, M. Belic
Format: Article
Language:English
Published: Elsevier 2019-12-01
Series:Results in Physics
Online Access:http://www.sciencedirect.com/science/article/pii/S2211379719323344
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spelling doaj-860d6a92a6f54319a2249b40da5b25c72020-11-25T01:11:16ZengElsevierResults in Physics2211-37972019-12-0115Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentialsHamdy I. Abdel-Gawad0A. Biswas1A.S. Alshomrani2M. Belic3Mathematics Department, Faculty of Sciences, Cairo university, Egypt; Corresponding author.Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-7500, USA; Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia; Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Shosse, Moscow 115409, Russian Federation; Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South AfricaDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaScience Program, Texas A&M University at Qatar, 23874 Doha, QatarWe consider coupled nonlinear Schrodinger equation (CNLSE) of the Gross-Pitaevskii-type, with linear mixing and nonlinear cross-phase modulation. Motivated by the study of matter waves in Bose-Einstein condensates and multicomponent (vectorial) nonlinear optical systems, we investigate the eigenvalue problem of the CNLSE with double external potentials in a self-defocusig Kerr medium. For this system, we obtain different kinds of wave structures induced by two injected beams, of physical relevance in nonlinear optics and Bose-Einstein condensation. Exact solutions are found by the extended unified method. The linear stability of these solutions is analyzed through the formulation of an eigenvalue problem. The spectral problem is constructed by perturbing the frequency of stationary solutions and by linearizing the resulting equations near the stationary (or steady) states. Our study may simulate experimental work on multiple injected laser beams in a medium with Kerr-type nonlinearity. Keywords: Coupled NLS equation, Double external potentials, The eigenvalue problem, Stabilityhttp://www.sciencedirect.com/science/article/pii/S2211379719323344
collection DOAJ
language English
format Article
sources DOAJ
author Hamdy I. Abdel-Gawad
A. Biswas
A.S. Alshomrani
M. Belic
spellingShingle Hamdy I. Abdel-Gawad
A. Biswas
A.S. Alshomrani
M. Belic
Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials
Results in Physics
author_facet Hamdy I. Abdel-Gawad
A. Biswas
A.S. Alshomrani
M. Belic
author_sort Hamdy I. Abdel-Gawad
title Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials
title_short Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials
title_full Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials
title_fullStr Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials
title_full_unstemmed Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials
title_sort optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials
publisher Elsevier
series Results in Physics
issn 2211-3797
publishDate 2019-12-01
description We consider coupled nonlinear Schrodinger equation (CNLSE) of the Gross-Pitaevskii-type, with linear mixing and nonlinear cross-phase modulation. Motivated by the study of matter waves in Bose-Einstein condensates and multicomponent (vectorial) nonlinear optical systems, we investigate the eigenvalue problem of the CNLSE with double external potentials in a self-defocusig Kerr medium. For this system, we obtain different kinds of wave structures induced by two injected beams, of physical relevance in nonlinear optics and Bose-Einstein condensation. Exact solutions are found by the extended unified method. The linear stability of these solutions is analyzed through the formulation of an eigenvalue problem. The spectral problem is constructed by perturbing the frequency of stationary solutions and by linearizing the resulting equations near the stationary (or steady) states. Our study may simulate experimental work on multiple injected laser beams in a medium with Kerr-type nonlinearity. Keywords: Coupled NLS equation, Double external potentials, The eigenvalue problem, Stability
url http://www.sciencedirect.com/science/article/pii/S2211379719323344
work_keys_str_mv AT hamdyiabdelgawad opticalsolitonsandstabilityanalysiswithcouplednonlinearschrodingersequationshavingdoubleexternalpotentials
AT abiswas opticalsolitonsandstabilityanalysiswithcouplednonlinearschrodingersequationshavingdoubleexternalpotentials
AT asalshomrani opticalsolitonsandstabilityanalysiswithcouplednonlinearschrodingersequationshavingdoubleexternalpotentials
AT mbelic opticalsolitonsandstabilityanalysiswithcouplednonlinearschrodingersequationshavingdoubleexternalpotentials
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