Dynamics of matter-wave solitons in a ratchet potential
  We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realises a flashing ratchet for matter-wave solitons. The average velocity of a soliton and the directed soliton current induced by the ratchet depend on the number of atoms in the soliton. We employ this feature to study collisions between ratchet-driven solitons and find that soliton transport can be induced through their interactions. In the regime when matter-wave solitons are narrow compared to the lattice period the ratchet dynamics is well described by the effective Hamiltonian theory. 
Dario Poletti, Tristram J. Alexander, Elena A. Ostrovskaya, Baowen Li,   Yuri S. Kivshar