  We study the effects of random scatterers on the ground state of the
one-dimensional Lieb-Liniger model of interacting bosons on the unit interval
in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation
survives even a strong random potential with a high density of scatterers. The
character of the wave function of the condensate, however, depends in an
essential way on the interplay between randomness and the strength of the
two-body interaction. For low density of scatterers or strong interactions the
wave function extends over the whole interval. High density of scatterers and
weak interaction, on the other hand, leads to localization of the wave function
in a fragmented subset of the interval.
