  We present a detailed numerical study of the dynamics of a disordered
one-dimensional Bose-Einstein condensates in position and momentum space. We
particularly focus on the region where non-linearity and disorder
simultaneously effect the time propagation of the condensate as well as the
possible interference between various parts of the matter wave. We report
oscillation between spatially extended and localized behavior for the
propagating condensate which dies down with increasing non-linearity. We also
report intriguing behavior of the phase fluctuation and the coherence
properties of the matter wave. We also briefly compare these behavior with that
of a two-dimensional condensate. We mention the relevance of our results to the
related experiments on Anderson localization and indicate the possibility of
future experiments
