  We consider time-dependent nonlinear Schroedinger equations subject to
smooth, lattice-periodic potentials plus additional confining potentials,
slowly varying on the lattice scale. After an appropriate scaling we study the
homogenization limit for vanishing lattice spacing. Assuming well prepared
initial data, the resulting effective dynamics is governed by a homogenized
nonlinear Schroedinger equation with an effective mass tensor depending on the
initially chosen Bloch eigenvalue. The given results rigorously justify the use
of the effective mass formalism for the description of Bose-Einstein
condensates on optical lattices.
