  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.
