At low temperature, a quasi-one-dimensional ensemble of atoms with attractive
interaction forms a bright soliton. When exposed to a weak and smooth external
potential, the shape of the soliton is hardly modified, but its center-of-mass
motion is affected. We show that in a spatially correlated disordered
potential, the quantum motion of a bright soliton displays Anderson
localization. The localization length can be much larger than the soliton size
and could be observed experimentally.Comment: version accepted for publication in Phys. Rev. Let