Dynamical localization of matter wave solitons in managed barrier   potentials
  The bright matter wave soliton propagation through a barrier with a rapidly oscillating position is investigated. The averaged over rapid oscillations Gross-Pitaevskii (GP) equation is derived. It is shown that the soliton is dynamically trapped by the effective double-barrier.   The analytical predictions for the soliton effective dynamics is confirmed by the numerical simulations of the full GP equation. 
Fatkhulla Kh. Abdullaev, Josselin Garnier