Dynamics of matter solitons in weakly modulated optical lattices

It is shown that matter solitons can be effectively managed by means of smooth variations of parameters of optical lattices in which the condensate is loaded. The phenomenon is based on the effect of lattice modulations on the carrier wave transporting the soliton and that is why it is well understood in terms of the effective mass approach, where a particular spatial configuration of the band structure is of primary importance. Linear, parabolic, and spatially localized modulations are considered as case examples. It is shown that these defects can originate an accelerating and oscillating motion of matter solitons as well as they can simulate soliton interactions with attractive and repulsive defects.