Statics, Dynamics and Manipulations of Bright Matter-Wave Solitons in   Optical Lattices
  Motivated by recent experimental achievement in the work with Bose-Einstein condensates (BECs), we consider bright matter-wave solitons, in the presence of a parabolic magnetic trap and a spatially periodic optical lattice (OL), in the attractive BEC. We examine pinned states of the soliton and their stability by means of perturbation theory. The analytical predictions are found to be in good agreement with numerical simulations. We then explore possibilities to use a time-modulated OL as a means of stopping and trapping a moving soliton, and of transferring an initially stationary soliton to a prescribed position by a moving OL. We also study the emission of radiation from the soliton moving across the combined magnetic trap and OL. We find that the soliton moves freely (without radiation) across a weak lattice, but suffers strong loss for stronger OLs. 
P.G. Kevrekidis, D.J. Frantzeskakis, R. Carretero-Gonzalez, B.A.   Malomed, G. Herring and A.R. Bishop