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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:
Journal Article: 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},
issn = {1050-2947},
number = 5,
volume = 92,
place = {United States},
year = {2015},
month = {11}
}

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Cited by: 4 works
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Works referenced in this record:

Dynamical Control of Matter-Wave Tunneling in Periodic Potentials
journal, November 2007


Inhibition of Light Tunneling in Waveguide Arrays
journal, April 2009


Compactons in Nonlinear Schrödinger Lattices with Strong Nonlinearity Management
journal, September 2010


Compacton matter waves in binary Bose gases under strong nonlinear management
journal, December 2014


Compactons: Solitons with finite wavelength
journal, February 1993


Nonlinear Dispersion and Compact Structures
journal, September 1994


Multidimensional Compactons
journal, January 2007


Stationary dark localized modes: Discrete nonlinear Schrödinger equations
journal, July 1999


Bright compact breathers
journal, June 2002


Dark compactlets
journal, July 2002


Discrete compactons: some exact results
journal, October 2002

  • Kevrekidis, P. G.; Konotop, V. V.; Bishop, A. R.
  • Journal of Physics A: Mathematical and General, Vol. 35, Issue 45
  • DOI: 10.1088/0305-4470/35/45/103

Shape profile of compactlike discrete breathers in nonlinear dispersive lattice systems
journal, December 2001


Exact localized eigenstates for an extended Bose-Hubbard model with pair-correlated hopping
journal, January 2012


Quantum dynamics of lattice states with compact support in an extended Bose-Hubbard model
journal, September 2013


Compactons and bistability in exciton-polariton condensates
journal, November 2012

  • Kartashov, Yaroslav V.; Konotop, Vladimir V.; Torner, Lluis
  • Physical Review B, Vol. 86, Issue 20
  • DOI: 10.1103/PhysRevB.86.205313

On the Existence of Solitary Traveling Waves for Generalized Hertzian Chains
journal, January 2012


Discrete flat-band solitons in the kagome lattice
journal, June 2013


Compactification tuning for nonlinear localized modes in sawtooth lattices
journal, September 2015


Observation of Localized States in Lieb Photonic Lattices
journal, June 2015


Ultracold Lattice Gases with Periodically Modulated Interactions
journal, November 2012


Exploring Unconventional Hubbard Models with Doubly Modulated Lattice Gases
journal, October 2014


Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions
journal, November 2014


From kinks to compactons
journal, September 2014


Compactification of Nonlinear Patterns and Waves
journal, December 2008


Emergence of Compact Structures in a Klein-Gordon Model
journal, January 2010


Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
journal, January 2003


Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
journal, January 2003

  • Abdullaev, Fatkhulla Kh.; Caputo, Jean Guy; Kraenkel, Robert A.
  • Physical Review A, Vol. 67, Issue 1
  • DOI: 10.1103/PhysRevA.67.013605

Regular spatial structures in arrays of Bose Einstein condensates induced by modulational instability
journal, December 2002

  • Baizakov, B. B.; Konotop, V. V.; Salerno, M.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 35, Issue 24
  • DOI: 10.1088/0953-4075/35/24/312

Multidimensional solitons in periodic potentials
journal, September 2003


Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling
journal, January 2009


Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
journal, March 2001


Nonlinear excitations in arrays of Bose-Einstein condensates
journal, September 2001


Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
journal, October 2002


Soliton Steering by Longitudinal Modulation of the Nonlinearity in Waveguide Arrays
journal, February 2010


Nonlinearity Management in Optics: Experiment, Theory, and Simulation
journal, July 2006


Modulational Instability in a Layered Kerr Medium: Theory and Experiment
journal, December 2006


Hamiltonian averaging for solitons with nonlinearity management
journal, October 2004


Superfluid-Insulator Transition in a Periodically Driven Optical Lattice
journal, December 2005


Finite-range corrections near a Feshbach resonance and their role in the Efimov effect
journal, August 2013


The higher-dimensional Ablowitz–Ladik model: From (non-)integrability and solitary waves to surprising collapse properties and more exotic solutions
journal, February 2012


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    Kinks and branes in models with hyperbolic interactions
    journal, September 2017

    • Bazeia, D.; Lima, Elisama E. M.; Losano, L.
    • International Journal of Modern Physics A, Vol. 32, Issue 26
    • DOI: 10.1142/s0217751x17501639

    Kinks and branes in models with hyperbolic interactions
    journal, September 2017

    • Bazeia, D.; Lima, Elisama E. M.; Losano, L.
    • International Journal of Modern Physics A, Vol. 32, Issue 26
    • DOI: 10.1142/s0217751x17501639