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It is shown that by properly designing the spatial dependence of thenonlinearity it is possible to induce long-living Bloch oscillations of alocalized wavepacket in a periodic potential. The results are supported both byanalytical and numerical investigations and are interpreted in terms of matterwave dynamics displaying dozens of oscillation periods without any visibledistortion of the wave packet.

Long-living Bloch oscillations of matter waves in optical lattices