Localization of solitons: linear response of the mean-field ground state to weak external potentials

Two aspects of bright matter–wave solitons in weak external potentials are discussed. First, we briefly review recent results on the Anderson localization of an entire soliton in disordered potentials, as a paradigmatic showcase of genuine quantum dynamics beyond simple perturbation theory. Second, we calculate the linear response of the mean-field soliton shape to a weak, but otherwise arbitrary, external potential, with a detailed application to lattice potentials.