Controllable soliton dragging by dynamical optical lattices

We report on the phenomenon of controllable soliton dragging by dynamical optical lattices induced by three imbalanced interfering plane waves. Because of such an imbalance, the transverse momentum of the lattice does not vanish, and thus the dynamical lattice can cause soliton dragging. The dragging rate is shown to depend on the amplitude and on the angle of incidence of the third plane wave making the optical lattice.