  We have experimentally studied the unstable dynamics of a harmonically
trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The
lifetime of the condensate in such a potential exhibits a dramatic dependence
on the quasimomentum state. This is unambiguously attributed to the onset of
dynamical instability, after a comparison with the predictions of the
Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid
appearance of complex structures in the atomic density profile, as a
consequence of the condensate phase uniformity breakdown.
