Time-Dependent Trapping of Solitons in Bose-Einstein Condensates
  We study the influence of a time-dependent potential on the motion of solitons in a quasi one-dimensional Bose-Einstein condensate by solving the corresponding Gross-Pitaevskii equation. For a suitable choice of the external potentials as well as the initial soliton characteristics time-dependent trapping of the soliton in a prescribed subarea of the condensate can be achieved. Adiabatic perturbation theory is shown to work remarkably well for large switching on times of the trapping potential and allows to perform a detailed study of the degree of trapping in the complete phase space of the soliton center. A remarkable spiral pattern of the degree of trapping as a function of the soliton characteristics is observed and explained. 
H.E. Nistazakis, D.J. Frantzeskakis, N. Brouzakis, F.K. Diakonos, P.   Schmelcher and J. Schmiedmayer