  We present a detailed numerical study of the effect of a disordered potential
on a confined one-dimensional Bose-Einstein condensate, in the framework of a
mean-field description. For repulsive interactions, we consider the
Thomas-Fermi and Gaussian limits and for attractive interactions the behavior
of soliton solutions. We find that the disorder average spatial extension of
the stationary density profile decreases with an increasing strength of the
disordered potential both for repulsive and attractive interactions among
bosons. In the Thomas Fermi limit, the suppression of transport is accompanied
by a strong localization of the bosons around the state k=0 in momentum space.
The time dependent density profiles differ considerably in the cases we have
considered. For attractive Bose-Einstein condensates, a bright soliton exists
with an overall unchanged shape, but a disorder dependent width. For weak
disorder, the soliton moves on and for a stronger disorder, it bounces back and
forth between high potential barriers.
