Macroscopic dynamics of a trapped Bose-Einstein condensate in the   presence of 1D and 2D optical lattices
  The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data. 
M. Kraemer, L. Pitaevskii, and S. Stringari