Abstract
By extending the Bloch-decomposition-based time-splitting spectral method we introduced earlier, we conduct numerical simulations of the dynamics of nonlinear Schrodinger equations subject to periodic and con. ning potentials. We consider this system as a two-scale asymptotic problem with different scalings of the nonlinearity. In particular we discuss (nonlinear) mass transfer between different Bloch bands and also present three-dimensional simulations for lattice Bose-Einstein condensates in the super fluid regime.