Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management

The existence of multidimensional lattice compactons in the discrete nonlinear Schr¨odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coup...

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Main Authors:	D’Ambroise, Jennie, Salerno, Mario, Kevrekidis, P. G., Abdullaev, Fatkhulla
Format:	Article
Language:	English
Published:	American Physical Society 2015
Subjects:	QC Physics
Online Access:	http://irep.iium.edu.my/45875/ http://irep.iium.edu.my/45875/ http://irep.iium.edu.my/45875/ http://irep.iium.edu.my/45875/1/PRA_2015_compactons.pdf

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spelling	iium-458752018-06-19T03:41:20Z http://irep.iium.edu.my/45875/ Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management D’Ambroise, Jennie Salerno, Mario Kevrekidis, P. G. Abdullaev, Fatkhulla QC Physics The existence of multidimensional lattice compactons in the discrete nonlinear Schr¨odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds.We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined. Other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. The possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed. American Physical Society 2015-11-19 Article PeerReviewed application/pdf en http://irep.iium.edu.my/45875/1/PRA_2015_compactons.pdf D’Ambroise, Jennie and Salerno, Mario and Kevrekidis, P. G. and Abdullaev, Fatkhulla (2015) Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management. The Physical Review A, 92. 053621-1. ISSN 1094-1622 (O), 1050-2947 (P) http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.053621 10.1103/PhysRevA.92.053621
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QC Physics
spellingShingle	QC Physics D’Ambroise, Jennie Salerno, Mario Kevrekidis, P. G. Abdullaev, Fatkhulla Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management
description	The existence of multidimensional lattice compactons in the discrete nonlinear Schr¨odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds.We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined. Other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. The possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.
format	Article
author	D’Ambroise, Jennie Salerno, Mario Kevrekidis, P. G. Abdullaev, Fatkhulla
author_facet	D’Ambroise, Jennie Salerno, Mario Kevrekidis, P. G. Abdullaev, Fatkhulla
author_sort	D’Ambroise, Jennie
title	Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management
title_short	Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management
title_full	Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management
title_fullStr	Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management
title_full_unstemmed	Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management
title_sort	multidimensional discrete compactons in nonlinear schr¨odinger lattices with strong nonlinearity management
publisher	American Physical Society
publishDate	2015
url	http://irep.iium.edu.my/45875/ http://irep.iium.edu.my/45875/ http://irep.iium.edu.my/45875/ http://irep.iium.edu.my/45875/1/PRA_2015_compactons.pdf
first_indexed	2023-09-18T21:05:18Z
last_indexed	2023-09-18T21:05:18Z
_version_	1777410892712902656

Multidimensional discrete compactons in nonlinear Schr¨odinger lattices with strong nonlinearity management

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