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.Comment: 28 pages, 9 figures, publishe

Alfimov E. G.

Bender C. M.

Burger S.

D. J. FRANTZESKAKIS

Donnelly R. J.

Einstein A.

Hasegawa A.

Kevrekidis P. G.

Kittel C.

Ostrovskii L. A.

P. G. KEVREKIDIS

Pitaevskii L. P.

Rapti Z.

Sulem C.

Williams J. E.

English

arXiv

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

Kevrekidis, PG

ScholarWorks@UMass Amherst

PATTERN FORMING DYNAMICAL INSTABILITIES OF BOSE–EINSTEIN CONDENSATES

This is the pre-published version harvested from arXiv. The published version is located at http://www.worldscinet.com/mplb/18/1805n06/S0217984904006809.htmlIn 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.173-20

Crossref

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

Kevrekidis, P.G.
Frantzeskakis, D.J.

Pergamos : Unified Institutional Repository / Digital Library Platform of the National and Kapodistrian University of Athens

Pattern forming dynamical instabilities of Bose-Einstein condensates

https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=2117&amp;context=math_faculty_pubs

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

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

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ScholarWorks@UMass Amherst

ScholarWorks@UMass Amherst

Crossref

Pergamos : Unified Institutional Repository / Digital Library Platform of the National and Kapodistrian University of Athens