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Pattern Forming Dynamical Instabilities of Bose-Einstein Condensates: A Short Review

P. G. Kevrekidis·D. J. Frantzeskakis
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Abstract

In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities of Bose-Einstein condensates in one- and two-dimensional settings. In particular, we illustrate the trapping conditions that allow the reduction of the three-dimensional, mean field description of the condensates (through the Gross-Pitaevskii equation) to such lower dimensional settings, as well as to lattice settings. We then go on to study the modulational instability in one dimension and the snaking/transverse instability in two dimensions as typical examples of long-wavelength perturbations that can destabilize the condensates and lead to the formation of patterns of coherent structures in them. Trains of solitons in one-dimension and vortex arrays in two-dimensions are prototypical examples of the resulting nonlinear waveforms, upon which we briefly touch at the end of this review.

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P. G. Kevrekidis, D. J. Frantzeskakis. 2004-06-26. Pattern Forming Dynamical Instabilities of Bose-Einstein Condensates: A Short Review. https://doi.org/10.1142/s0217984904006809

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