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Spatial coherence resonance on diffusive and small-world networks of Hodgkin–Huxley neurons
Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin–Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spa...

Disk-shaped Bose–Einstein condensates in the presence of an harmonic trap and an optical lattice

Chaos 18, 023101 (2008); doi:10.1063/1.2897311

Published 9 April 2008

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Todd Kapitula,1 Panayotis G. Kevrekidis,2 and D. J. Frantzeskakis3
1Department of Mathematics and Statistics, Calvin College, Grand Rapids, Michigan 49456, USA
2Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
3Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
We study the existence and stability of solutions of the two-dimensional nonlinear Schrödinger equation in the combined presence of a parabolic and a periodic potential. The motivating physical example consists of Bose–Einstein condensates confined in an harmonic (e.g., magnetic) trap and an optical lattice. By connecting the nonlinear problem with the underlying linear spectrum, we examine the bifurcation of nonlinear modes out of the linear ones for both focusing and defocusing nonlinearities. In particular, we find real-valued solutions (such as multipoles) and complex-valued ones (such as vortices). A primary motivation of the present work is to develop “rules of thumb” about what waveforms to expect emerging in the nonlinear problem and about the stability of those modes. As a case example of the latter, we find that among the real-valued solutions, the one with larger norm for a fixed value of the chemical potential is expected to be unstable. ©2008 American Institute of Physics
History: Received 12 November 2007; accepted 22 February 2008; published 9 April 2008
Permalink: http://link.aip.org/link/?CHAOEH/18/023101/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.75.Lm
    Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations
  • 03.75.Kk
    Dynamic properties of Bose-Einstein condensates
  • 05.45.Yv
    Solitons
  • YEAR: 2008

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
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