Integrability of a general Gross-Pitaevskii equation and exact solitonic solutions of a Bose-Einstein condensate in a periodic potential

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Abstract

We consider a general form of the Gross-Pitaevskii equation with time- and space-dependent effective mass, external potential and strength of interatomic interaction. Using the inverse-scattering method, we derive the integrability condition of this equation within a general scheme that can be used to find exact solutions of a wide range of linear and nonlinear partial differential equations. We use this condition to derive exact solitonic solutions of the one-dimensional time-dependent Gross-Pitaevskii equation corresponding to a Bose-Einstein condensate trapped by a periodic potential. Both attractive and repulsive interatomic interactions are considered. The values of the parameters of the potential can be chosen such that the periodic potential becomes almost identical to that of an optical lattice.

Original languageEnglish
Pages (from-to)2710-2716
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume373
Issue number31
DOIs
Publication statusPublished - Jul 20 2009

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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