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:
-
- Amherst College, MA (United States)
- Univ. of Salerno (Italy)
- Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- International Islamic Univ. of Malaysia (Malaysia)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (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 - Atomic, Molecular, and Optical Physics
- 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. https://doi.org/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. https://doi.org/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 - Atomic, Molecular, and Optical Physics},
number = 5,
volume = 92,
place = {United States},
year = {Thu Nov 19 00:00:00 EST 2015},
month = {Thu Nov 19 00:00:00 EST 2015}
}
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Works referenced in this record:
Dynamical Control of Matter-Wave Tunneling in Periodic Potentials
journal, November 2007
- Lignier, H.; Sias, C.; Ciampini, D.
- Physical Review Letters, Vol. 99, Issue 22
Inhibition of Light Tunneling in Waveguide Arrays
journal, April 2009
- Szameit, A.; Kartashov, Y. V.; Dreisow, F.
- Physical Review Letters, Vol. 102, Issue 15
Compactons in Nonlinear Schrödinger Lattices with Strong Nonlinearity Management
journal, September 2010
- Abdullaev, F. Kh.; Kevrekidis, P. G.; Salerno, M.
- Physical Review Letters, Vol. 105, Issue 11
Compacton matter waves in binary Bose gases under strong nonlinear management
journal, December 2014
- Abdullaev, F. Kh.; Hadi, M. S. A.; Salerno, M.
- Physical Review A, Vol. 90, Issue 6
Compactons: Solitons with finite wavelength
journal, February 1993
- Rosenau, Philip; Hyman, James M.
- Physical Review Letters, Vol. 70, Issue 5
Nonlinear Dispersion and Compact Structures
journal, September 1994
- Rosenau, Philip
- Physical Review Letters, Vol. 73, Issue 13
Multidimensional Compactons
journal, January 2007
- Rosenau, Philip; Hyman, James M.; Staley, Martin
- Physical Review Letters, Vol. 98, Issue 2
Stationary dark localized modes: Discrete nonlinear Schrödinger equations
journal, July 1999
- Konotop, V. V.; Takeno, S.
- Physical Review E, Vol. 60, Issue 1
Bright compact breathers
journal, June 2002
- Kevrekidis, P. G.; Konotop, V. V.
- Physical Review E, Vol. 65, Issue 6
Dark compactlets
journal, July 2002
- Kevrekidis, P. G.; Konotop, V. V.; Takeno, S.
- Physics Letters A, Vol. 299, Issue 2-3
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
Shape profile of compactlike discrete breathers in nonlinear dispersive lattice systems
journal, December 2001
- Dey, B.; Eleftheriou, M.; Flach, S.
- Physical Review E, Vol. 65, Issue 1
Exact localized eigenstates for an extended Bose-Hubbard model with pair-correlated hopping
journal, January 2012
- Jason, Peter; Johansson, Magnus
- Physical Review A, Vol. 85, Issue 1
Quantum dynamics of lattice states with compact support in an extended Bose-Hubbard model
journal, September 2013
- Jason, Peter; Johansson, Magnus
- Physical Review A, Vol. 88, Issue 3
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
On the solitary wave pulse in a chain of beads
journal, January 2005
- English, J. M.; Pego, R. L.
- Proceedings of the American Mathematical Society, Vol. 133, Issue 6, p. 1763-1768
On the Existence of Solitary Traveling Waves for Generalized Hertzian Chains
journal, January 2012
- Stefanov, Atanas; Kevrekidis, Panayotis
- Journal of Nonlinear Science, Vol. 22, Issue 3
Discrete flat-band solitons in the kagome lattice
journal, June 2013
- Vicencio, Rodrigo A.; Johansson, Magnus
- Physical Review A, Vol. 87, Issue 6
Compactification tuning for nonlinear localized modes in sawtooth lattices
journal, September 2015
- Johansson, Magnus; Naether, Uta; Vicencio, Rodrigo A.
- Physical Review E, Vol. 92, Issue 3
Observation of Localized States in Lieb Photonic Lattices
journal, June 2015
- Vicencio, Rodrigo A.; Cantillano, Camilo; Morales-Inostroza, Luis
- Physical Review Letters, Vol. 114, Issue 24
Ultracold Lattice Gases with Periodically Modulated Interactions
journal, November 2012
- Rapp, Ákos; Deng, Xiaolong; Santos, Luis
- Physical Review Letters, Vol. 109, Issue 20
Exploring Unconventional Hubbard Models with Doubly Modulated Lattice Gases
journal, October 2014
- Greschner, Sebastian; Santos, Luis; Poletti, Dario
- Physical Review Letters, Vol. 113, Issue 18
Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions
journal, November 2014
- Greschner, S.; Sun, G.; Poletti, D.
- Physical Review Letters, Vol. 113, Issue 21
From kinks to compactons
journal, September 2014
- Bazeia, D.; Losano, L.; Marques, M. A.
- Physics Letters B, Vol. 736
Compactification of Nonlinear Patterns and Waves
journal, December 2008
- Rosenau, Philip; Kashdan, Eugene
- Physical Review Letters, Vol. 101, Issue 26
Emergence of Compact Structures in a Klein-Gordon Model
journal, January 2010
- Rosenau, Philip; Kashdan, Eugene
- Physical Review Letters, Vol. 104, Issue 3
Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
journal, January 2003
- Saito, Hiroki; Ueda, Masahito
- Physical Review Letters, Vol. 90, Issue 4
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
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
Multidimensional solitons in periodic potentials
journal, September 2003
- Baizakov, B. B.; Malomed, B. A.; Salerno, M.
- Europhysics Letters (EPL), Vol. 63, Issue 5
Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling
journal, January 2009
- Öster, Michael; Johansson, Magnus
- Physica D: Nonlinear Phenomena, Vol. 238, Issue 1
Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
journal, March 2001
- Trombettoni, Andrea; Smerzi, Augusto
- Physical Review Letters, Vol. 86, Issue 11
Nonlinear excitations in arrays of Bose-Einstein condensates
journal, September 2001
- Abdullaev, F. Kh.; Baizakov, B. B.; Darmanyan, S. A.
- Physical Review A, Vol. 64, Issue 4
Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
journal, October 2002
- Alfimov, G. L.; Kevrekidis, P. G.; Konotop, V. V.
- Physical Review E, Vol. 66, Issue 4
Soliton Steering by Longitudinal Modulation of the Nonlinearity in Waveguide Arrays
journal, February 2010
- Assanto, Gaetano; Cisneros, Luis A.; Minzoni, Antonmaria A.
- Physical Review Letters, Vol. 104, Issue 5
Nonlinearity Management in Optics: Experiment, Theory, and Simulation
journal, July 2006
- Centurion, Martin; Porter, Mason A.; Kevrekidis, P. G.
- Physical Review Letters, Vol. 97, Issue 3
Modulational Instability in a Layered Kerr Medium: Theory and Experiment
journal, December 2006
- Centurion, Martin; Porter, Mason A.; Pu, Ye
- Physical Review Letters, Vol. 97, Issue 23
Hamiltonian averaging for solitons with nonlinearity management
journal, October 2004
- Pelinovsky, D. E.; Kevrekidis, P. G.; Frantzeskakis, D. J.
- Physical Review E, Vol. 70, Issue 4
Superfluid-Insulator Transition in a Periodically Driven Optical Lattice
journal, December 2005
- Eckardt, André; Weiss, Christoph; Holthaus, Martin
- Physical Review Letters, Vol. 95, Issue 26
Emergent Nonlinear Phenomena in Bose-Einstein Condensates
book, January 2008
- Kevrekidis, Panayotis G.; Frantzeskakis, Dimitri J.; Carretero-González, Ricardo
- Atomic, Optical, and Plasma Physics
Finite-range corrections near a Feshbach resonance and their role in the Efimov effect
journal, August 2013
- Dyke, P.; Pollack, S. E.; Hulet, R. G.
- Physical Review A, Vol. 88, Issue 2
The higher-dimensional Ablowitz–Ladik model: From (non-)integrability and solitary waves to surprising collapse properties and more exotic solutions
journal, February 2012
- Kevrekidis, P. G.; Herring, G. J.; Lafortune, S.
- Physics Letters A, Vol. 376, Issue 8-9
Works referencing / citing this record:
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
Kinks and branes in models with hyperbolic interactions
text, January 2017
- Bazeia, D.; Lima, Elisama E. M.; Losano, L.
- arXiv