Dynamics and Manipulation of Matter-Wave Solitons in Optical   Superlattices
  We analyze the existence and stability of bright, dark, and gap matter-wave solitons in optical superlattices. Then, using these properties, we show that (time-dependent) ``dynamical superlattices'' can be used to controllably place, guide, and manipulate these solitons. In particular, we use numerical experiments to displace solitons by turning on a secondary lattice structure, transfer solitons from one location to another by shifting one superlattice substructure relative to the other, and implement solitonic ``path-following'', in which a matter wave follows the time-dependent lattice substructure into oscillatory motion. 
Mason A. Porter, P. G. Kevrekidis, R. Carretero-Gonz\'alez, and D. J.   Frantzeskakis