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

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)

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	7021/45875
Uncontrolled Keywords:	nonlinear Schrodinger lattices
Subjects:	Q Science > QC Physics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Physics
Depositing User:	Prof Fatkhulla Abdullaev
Date Deposited:	25 Nov 2015 10:45
Last Modified:	19 Jun 2018 11:41
URI:	http://irep.iium.edu.my/id/eprint/45875

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