Dynamics of matter solitons in weakly modulated optical lattices

It was shown that matter solitons can be effectively managed by smooth variation of parameters of optical lattices in which the atomic condensate is embedded. The phenomenon is based on the effect of the lattice modulation of the carrier wave that transports the soliton and thus can be well described in terms of the effective mass approach, where a specific form of the band structure is of primary importance. We considered linear and parabolic modulation to demonstrate the possibilities of management of matter solitons.