Dynamics of matter solitons in modulated optical lattices

In the present work this situation is studied analytically and numerically. In particular, we show that this is a way of managing the dynamics of matter waves - making them accelerating, oscillating, etc. In a general case, to describe the effect of the modulation, we compute dependence of the gap structure, of the group velocity of the Bloch wave, and of the effective mass of the soliton on spatial variable. The effective mass approach appears to be a useful analytical tool in this case, as well. The main physical interest of this situation consists of the fact that now the defect affects a matter soliton by interacting with its carrier wave and gives origin to various resonant effects