Matter waves inside periodic potentials are well known from solid-state physics, where
electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates …

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of
correct self-consistent description of arbitrary systems with Bose-Einstein condensate are …

The aim of this review is to introduce the reader to some of the physical notions and the
mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein …

Abstract Superflow of a Bose–Einstein condensate in an optical lattice is represented by a
Bloch wave, a plane wave with periodic modulation of the amplitude. We review the …

We investigate the band structure of a Bose-Einstein condensate in a one-dimensional
periodic potential by calculating stationary solutions of the Gross-Pitaevskii equation, which …

We systematically study the properties of lattice solitons in Bose-Einstein condensates with
either attractive or repulsive atom interactions. This is done, by exactly solving the mean …

We present a theory of hysteretic phenomena in Bose gases, using superfluidity in one-
dimensional rings and in optical lattices as primary examples. Through this study we are …

We discuss interacting and noninteracting one dimensional atomic systems trapped in an
optical lattice plus a parabolic potential. We show that, in the tight-binding approximation …

Geometric frustration of particle motion in a kagome lattice causes the single-particle band
structure to have a flat s-orbital band. We probe this band structure by placing a Bose …

We show that the phenomenon of modulational instability in arrays of Bose–Einstein
condensates confined to optical lattices gives rise to coherent spatial structures of localized …