Coherent structures of Bose-Einstein condensates in optical lattices

We propose to employ the phenomenon of modulational instability in order to create regularly arranged localized excitations in arrays of Bose-Einstein condensates. These excitations are narrow tubes in 2D and small hollows in 3D arrays filled in with the condensed atoms of much greater density compared to surrounding array sites. As the regions with high atomic concentration develop due to the modulational instability, they can be preserved by increasing the strength of the optical lattice. Theoretical model, based on the multiple scale expansion, describes the main features of the phenomenon. Analytical predictions are confirmed by numerical simulations of the Gross-Pitaevskii equation.