Role of the Mean-field in Bloch Oscillations of a Bose-Einstein   Condensate in an Optical Lattice and Harmonic Trap
  Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in the Bloch-like oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses the dispersion of the condensate in momentum space. When the mean field becomes large, soliton and vortex structures appear in the condensate wavefunction. 
R. Zhang, R. E. Sapiro, R. R. Mhaskar, G. Raithel