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We show that the phenomenon of modulational instability in arrays ofBose-Einstein condensates confined to optical lattices gives rise to coherentspatial structures of localized excitations. These excitations represent thindisks in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in withcondensed atoms of much greater density compared to surrounding array sites.Aspects of the developed pattern depend on the initial distribution function ofthe condensate over the optical lattice, corresponding to particular points ofthe Brillouin zone. The long-time behavior of the spatial structures emergingdue to modulational instability is characterized by the periodic recurrence tothe initial low-density state in a finite optical lattice. We propose a simpleway to retain the localized spatial structures with high atomic concentration,which may be of interest for applications. Theoretical model, based on themultiple scale expansion, describes the basic features of the phenomenon.Results of numerical simulations confirm the analytical predictions.Comment: 17 pages, 13 figure

Regular spatial structures in arrays of Bose Einstein condensates induced by modulational instability