Dynamics of kicked matter-wave solitons in an optical lattice
  We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose-Einstein condensate trapped in a optical lattice. The resulting soliton's dynamics is studied within the framework of the time-dependent nonpolynomial Schrodinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice. 
A. Cetoli, L. Salasnich, B.A. Malomed, F. Toigo