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The hydrodynamic equations of superfluids for a weakly interacting Bose gasare generalized to include the effects of periodic optical potentials producedby stationary laser beams. The new equations are characterized by arenormalized interaction coupling constant and by an effective mass accountingfor the inertia of the system along the laser direction. For large laserintensities the effective mass is directly related to the tunneling ratebetween two consecutive wells. The predictions for the frequencies of thecollective modes of a condensate confined by a magnetic harmonic trap arediscussed for both 1D and 2D optical lattices and compared with recentexperimental data.Comment: 4 pages, 2 postscript figure

Macroscopic Dynamics of a Trapped Bose-Einstein Condensate in the Presence of 1D and 2D Optical Lattices