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We present a detailed numerical study of the dynamics of a disorderedone-dimensional Bose-Einstein condensates in position and momentum space. Weparticularly focus on the region where non-linearity and disordersimultaneously effect the time propagation of the condensate as well as thepossible interference between various parts of the matter wave. We reportoscillation between spatially extended and localized behavior for thepropagating condensate which dies down with increasing non-linearity. We alsoreport intriguing behavior of the phase fluctuation and the coherenceproperties of the matter wave. We also briefly compare these behavior with thatof a two-dimensional condensate. We mention the relevance of our results to therelated experiments on Anderson localization and indicate the possibility offuture experiments

Density, phase and coherence properties of a low dimensional Bose-Einstein systems moving in a disordered potential