  We analyze the Floquet-Bloch matter-wave spectrum of Bose-Einstein
condensates loaded into single-periodic optical lattices and double-periodic
superlattices. In the framework of the Gross-Pitaevskii equation, we describe
the structure and analyze the mobility properties of dark matter-wave solitons
residing on the background of extended nonlinear Bloch-type states. We
demonstrate that interaction between dark solitons can be effectively
controlled in optical superlattices.
