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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2015
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my.iium.irep.45875 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 |
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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/45875/1/PRA_2015_compactons.pdf http://irep.iium.edu.my/45875/ http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.053621 |
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1643616861923835904 |
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13.18916 |