Achilleos, V. and Theocharis, G. and Kevrekidis, P. G. and Karachalios, N. I. and Diakonos, F. K. and Frantzeskakis, D. J. (2011) Stationary states of a nonlinear Schrödinger lattice with a harmonic trap. Journal of Mathematical Physics, 52 (9). Art. No. 092701. ISSN 0022-2488 http://resolver.caltech.edu/CaltechAUTHORS:20111205-090639967
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We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that – in the discrete regime – all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only in the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed.
|Additional Information:||© 2011 American Institute of Physics. Received 11 March 2011; accepted 24 July 2011; published online 8 September 2011. G.T. acknowledges support from the Alexander S. Onassis Foundation. P.G.K. gratefully acknowledges support from NSF-DMS-0349023, NSF-DMS-0806762, NSF-CMMI-1000337, and from Alexander von Humboldt and Alexander S. Onassis Foundations. The work of F.K.D. and D.J.F. was partially supported by the Special Account for Research Grants of the University of Athens.|
|Subject Keywords:||bifurcation, Bose-Einstein condensation, lattice theory, nonlinear equations, Schrodinger equation, solitons|
|Classification Code:||PACS: 03.65.Ge; 05.45.-a; 05.45.Yv|
|Official Citation:||Stationary states of a nonlinear Schrödinger lattice with a harmonic trap V. Achilleos, G. Theocharis, P. G. Kevrekidis, N. I. Karachalios, F. K. Diakonos, and D. J. Frantzeskakis J. Math. Phys. 52, 092701 (2011); doi:10.1063/1.3625953 (25 pages) Online Publication Date: 8 September 2011|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||05 Dec 2011 17:50|
|Last Modified:||26 Dec 2012 14:33|
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