  Our aim is to analyze the various energy functionals appearing in the physics
literature and describing the behavior of a Bose-Einstein condensate in an
optical lattice. We want to justify the use of some reduced models. For that
purpose, we will use the semi-classical analysis developed for linear problems
related to the Schr\"odinger operator with periodic potential or multiple wells
potentials. We justify, in some asymptotic regimes, the reduction to low
dimensional problems and analyze the reduced problems.
