Controlling the motion of dark solitons by means of periodic potentials: application to Bose-Einstein condensates in optical lattices.

We demonstrate that the motion of dark solitons (DSs) can be controlled by means of periodic potentials. The mechanism is realized in terms of cigar-shaped Bose-Einstein condensates confined in a harmonic magnetic potential, in the presence of an optical lattice (OL). In the case when the OL period is comparable to the width of the DS, we demonstrate that (a) a moving dark soliton can be captured, switching on the OL, and (b) a stationary DS can be dragged by a moving OL.