Long-living Bloch oscillations of matter waves in optical lattices
  It is shown that by properly designing the spatial dependence of the nonlinearity it is possible to induce long-living Bloch oscillations of a localized wavepacket in a periodic potential. The results are supported both by analytical and numerical investigations and are interpreted in terms of matter wave dynamics displaying dozens of oscillation periods without any visible distortion of the wave packet. 
M. Salerno, V. V. Konotop, Yu. V. Bludov