Dynamics and manipulation of matter-wave solitons in optical superlattices

We study 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.