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Title: Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

Abstract

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger 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. We also found that 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. Finally, 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.

Authors:
 [1];  [2];  [3];  [4]
  1. Amherst College, MA (United States)
  2. Univ. of Salerno (Italy)
  3. Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  4. International Islamic Univ. of Malaysia (Malaysia)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1234821
Alternate Identifier(s):
OSTI ID: 1226505
Report Number(s):
LA-UR-15-26190
Journal ID: ISSN 1050-2947; PLRAAN; TRN: US1600433
Grant/Contract Number:  
NSF-DMS-1312856; BSF-2010239; FA9550-12-1-0332; AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 92; Journal Issue: 5; Journal ID: ISSN 1050-2947
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING

Citation Formats

D'Ambroise, J., Salerno, M., Kevrekidis, P. G., and Abdullaev, F. Kh. Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management. United States: N. p., 2015. Web. doi:10.1103/PhysRevA.92.053621.
D'Ambroise, J., Salerno, M., Kevrekidis, P. G., & Abdullaev, F. Kh. Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management. United States. doi:10.1103/PhysRevA.92.053621.
D'Ambroise, J., Salerno, M., Kevrekidis, P. G., and Abdullaev, F. Kh. Thu . "Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management". United States. doi:10.1103/PhysRevA.92.053621. https://www.osti.gov/servlets/purl/1234821.
@article{osti_1234821,
title = {Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management},
author = {D'Ambroise, J. and Salerno, M. and Kevrekidis, P. G. and Abdullaev, F. Kh.},
abstractNote = {The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger 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. We also found that 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. Finally, 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.},
doi = {10.1103/PhysRevA.92.053621},
journal = {Physical Review. A},
number = 5,
volume = 92,
place = {United States},
year = {2015},
month = {11}
}

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