Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.; Abdullaev, F. Kh.

doi:10.1103/PhysRevA.92.053621

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

Journal Article · Thu Nov 19 00:00:00 EST 2015 · Physical Review A - Atomic, Molecular, and Optical Physics

DOI:https://doi.org/10.1103/PhysRevA.92.053621· OSTI ID:1234821

D'Ambroise, J. ^[1]; Salerno, M. ^[2]; Kevrekidis, P. G. ^[3]; Abdullaev, F. Kh. ^[4]

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)

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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: NSF-DMS-1312856; BSF-2010239; FA9550-12-1-0332; AC52-06NA25396

OSTI ID:: 1234821

Alternate ID(s):: OSTI ID: 1226505

Report Number(s):: LA-UR-15-26190; PLRAAN; TRN: US1600433

Journal Information:: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 92, Issue 5; ISSN 1050-2947

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 6 works

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References (42)

Dynamical Control of Matter-Wave Tunneling in Periodic Potentials Lignier, H.; Sias, C.; Ciampini, D. Physical Review Letters, Vol. 99, Issue 22 https://doi.org/10.1103/PhysRevLett.99.220403	journal	November 2007
Inhibition of Light Tunneling in Waveguide Arrays Szameit, A.; Kartashov, Y. V.; Dreisow, F. Physical Review Letters, Vol. 102, Issue 15 https://doi.org/10.1103/PhysRevLett.102.153901	journal	April 2009
Compactons in Nonlinear Schrödinger Lattices with Strong Nonlinearity Management Abdullaev, F. Kh.; Kevrekidis, P. G.; Salerno, M. Physical Review Letters, Vol. 105, Issue 11 https://doi.org/10.1103/PhysRevLett.105.113901	journal	September 2010
Compacton matter waves in binary Bose gases under strong nonlinear management Abdullaev, F. Kh.; Hadi, M. S. A.; Salerno, M. Physical Review A, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevA.90.063637	journal	December 2014
Compactons: Solitons with finite wavelength Rosenau, Philip; Hyman, James M. Physical Review Letters, Vol. 70, Issue 5 https://doi.org/10.1103/PhysRevLett.70.564	journal	February 1993
Nonlinear Dispersion and Compact Structures Rosenau, Philip Physical Review Letters, Vol. 73, Issue 13 https://doi.org/10.1103/PhysRevLett.73.1737	journal	September 1994
Multidimensional Compactons Rosenau, Philip; Hyman, James M.; Staley, Martin Physical Review Letters, Vol. 98, Issue 2 https://doi.org/10.1103/PhysRevLett.98.024101	journal	January 2007
Stationary dark localized modes: Discrete nonlinear Schrödinger equations Konotop, V. V.; Takeno, S. Physical Review E, Vol. 60, Issue 1 https://doi.org/10.1103/PhysRevE.60.1001	journal	July 1999
Bright compact breathers Kevrekidis, P. G.; Konotop, V. V. Physical Review E, Vol. 65, Issue 6 https://doi.org/10.1103/PhysRevE.65.066614	journal	June 2002
Dark compactlets Kevrekidis, P. G.; Konotop, V. V.; Takeno, S. Physics Letters A, Vol. 299, Issue 2-3 https://doi.org/10.1016/S0375-9601(02)00704-1	journal	July 2002
Discrete compactons: some exact results Kevrekidis, P. G.; Konotop, V. V.; Bishop, A. R. Journal of Physics A: Mathematical and General, Vol. 35, Issue 45 https://doi.org/10.1088/0305-4470/35/45/103	journal	October 2002
Shape profile of compactlike discrete breathers in nonlinear dispersive lattice systems Dey, B.; Eleftheriou, M.; Flach, S. Physical Review E, Vol. 65, Issue 1 https://doi.org/10.1103/PhysRevE.65.017601	journal	December 2001
Exact localized eigenstates for an extended Bose-Hubbard model with pair-correlated hopping Jason, Peter; Johansson, Magnus Physical Review A, Vol. 85, Issue 1 https://doi.org/10.1103/PhysRevA.85.011603	journal	January 2012
Quantum dynamics of lattice states with compact support in an extended Bose-Hubbard model Jason, Peter; Johansson, Magnus Physical Review A, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevA.88.033605	journal	September 2013
Compactons and bistability in exciton-polariton condensates Kartashov, Yaroslav V.; Konotop, Vladimir V.; Torner, Lluis Physical Review B, Vol. 86, Issue 20 https://doi.org/10.1103/PhysRevB.86.205313	journal	November 2012
On the solitary wave pulse in a chain of beads English, J. M.; Pego, R. L. Proceedings of the American Mathematical Society, Vol. 133, Issue 6, p. 1763-1768 https://doi.org/10.1090/S0002-9939-05-07851-2	journal	January 2005
On the Existence of Solitary Traveling Waves for Generalized Hertzian Chains Stefanov, Atanas; Kevrekidis, Panayotis Journal of Nonlinear Science, Vol. 22, Issue 3 https://doi.org/10.1007/s00332-011-9119-9	journal	January 2012
Discrete flat-band solitons in the kagome lattice Vicencio, Rodrigo A.; Johansson, Magnus Physical Review A, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevA.87.061803	journal	June 2013
Compactification tuning for nonlinear localized modes in sawtooth lattices Johansson, Magnus; Naether, Uta; Vicencio, Rodrigo A. Physical Review E, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevE.92.032912	journal	September 2015
Observation of Localized States in Lieb Photonic Lattices Vicencio, Rodrigo A.; Cantillano, Camilo; Morales-Inostroza, Luis Physical Review Letters, Vol. 114, Issue 24 https://doi.org/10.1103/PhysRevLett.114.245503	journal	June 2015
Ultracold Lattice Gases with Periodically Modulated Interactions Rapp, Ákos; Deng, Xiaolong; Santos, Luis Physical Review Letters, Vol. 109, Issue 20 https://doi.org/10.1103/PhysRevLett.109.203005	journal	November 2012
Exploring Unconventional Hubbard Models with Doubly Modulated Lattice Gases Greschner, Sebastian; Santos, Luis; Poletti, Dario Physical Review Letters, Vol. 113, Issue 18 https://doi.org/10.1103/PhysRevLett.113.183002	journal	October 2014
Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions Greschner, S.; Sun, G.; Poletti, D. Physical Review Letters, Vol. 113, Issue 21 https://doi.org/10.1103/PhysRevLett.113.215303	journal	November 2014
From kinks to compactons Bazeia, D.; Losano, L.; Marques, M. A. Physics Letters B, Vol. 736 https://doi.org/10.1016/j.physletb.2014.08.015	journal	September 2014
Compactification of Nonlinear Patterns and Waves Rosenau, Philip; Kashdan, Eugene Physical Review Letters, Vol. 101, Issue 26 https://doi.org/10.1103/PhysRevLett.101.264101	journal	December 2008
Emergence of Compact Structures in a Klein-Gordon Model Rosenau, Philip; Kashdan, Eugene Physical Review Letters, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevLett.104.034101	journal	January 2010
Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate Saito, Hiroki; Ueda, Masahito Physical Review Letters, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevLett.90.040403	journal	January 2003
Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length Abdullaev, Fatkhulla Kh.; Caputo, Jean Guy; Kraenkel, Robert A. Physical Review A, Vol. 67, Issue 1 https://doi.org/10.1103/PhysRevA.67.013605	journal	January 2003
Regular spatial structures in arrays of Bose Einstein condensates induced by modulational instability Baizakov, B. B.; Konotop, V. V.; Salerno, M. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 35, Issue 24 https://doi.org/10.1088/0953-4075/35/24/312	journal	December 2002
Multidimensional solitons in periodic potentials Baizakov, B. B.; Malomed, B. A.; Salerno, M. Europhysics Letters (EPL), Vol. 63, Issue 5 https://doi.org/10.1209/epl/i2003-00579-4	journal	September 2003
Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling Öster, Michael; Johansson, Magnus Physica D: Nonlinear Phenomena, Vol. 238, Issue 1 https://doi.org/10.1016/j.physd.2008.08.006	journal	January 2009
Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates Trombettoni, Andrea; Smerzi, Augusto Physical Review Letters, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevLett.86.2353	journal	March 2001
Nonlinear excitations in arrays of Bose-Einstein condensates Abdullaev, F. Kh.; Baizakov, B. B.; Darmanyan, S. A. Physical Review A, Vol. 64, Issue 4 https://doi.org/10.1103/PhysRevA.64.043606	journal	September 2001
Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential Alfimov, G. L.; Kevrekidis, P. G.; Konotop, V. V. Physical Review E, Vol. 66, Issue 4 https://doi.org/10.1103/PhysRevE.66.046608	journal	October 2002
Soliton Steering by Longitudinal Modulation of the Nonlinearity in Waveguide Arrays Assanto, Gaetano; Cisneros, Luis A.; Minzoni, Antonmaria A. Physical Review Letters, Vol. 104, Issue 5 https://doi.org/10.1103/PhysRevLett.104.053903	journal	February 2010
Nonlinearity Management in Optics: Experiment, Theory, and Simulation Centurion, Martin; Porter, Mason A.; Kevrekidis, P. G. Physical Review Letters, Vol. 97, Issue 3 https://doi.org/10.1103/PhysRevLett.97.033903	journal	July 2006
Modulational Instability in a Layered Kerr Medium: Theory and Experiment Centurion, Martin; Porter, Mason A.; Pu, Ye Physical Review Letters, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevLett.97.234101	journal	December 2006
Hamiltonian averaging for solitons with nonlinearity management Pelinovsky, D. E.; Kevrekidis, P. G.; Frantzeskakis, D. J. Physical Review E, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevE.70.047604	journal	October 2004
Superfluid-Insulator Transition in a Periodically Driven Optical Lattice Eckardt, André; Weiss, Christoph; Holthaus, Martin Physical Review Letters, Vol. 95, Issue 26 https://doi.org/10.1103/PhysRevLett.95.260404	journal	December 2005
Emergent Nonlinear Phenomena in Bose-Einstein Condensates Kevrekidis, Panayotis G.; Frantzeskakis, Dimitri J.; Carretero-González, Ricardo Atomic, Optical, and Plasma Physics https://doi.org/10.1007/978-3-540-73591-5	book	January 2008
Finite-range corrections near a Feshbach resonance and their role in the Efimov effect Dyke, P.; Pollack, S. E.; Hulet, R. G. Physical Review A, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevA.88.023625	journal	August 2013
The higher-dimensional Ablowitz–Ladik model: From (non-)integrability and solitary waves to surprising collapse properties and more exotic solutions Kevrekidis, P. G.; Herring, G. J.; Lafortune, S. Physics Letters A, Vol. 376, Issue 8-9 https://doi.org/10.1016/j.physleta.2011.11.023	journal	February 2012

Cited By (2)

Kinks and branes in models with hyperbolic interactions Bazeia, D.; Lima, Elisama E. M.; Losano, L. International Journal of Modern Physics A, Vol. 32, Issue 26 https://doi.org/10.1142/s0217751x17501639	journal	September 2017
Kinks and branes in models with hyperbolic interactions Bazeia, D.; Lima, Elisama E. M.; Losano, L. arXiv https://doi.org/10.48550/arxiv.1705.02839	text	January 2017

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