Linear and Nonlinear Anderson Localization in a Curved Potential

Disorder induced localization in the presence of nonlinearity and curvature is investigated. The time-resolved three-dimensional expansion of a wave packet in a bent cigar shaped potential with a focusing Kerr-like interaction term and Gaussian disorder is numerically analyzed. A self-consistent analytical theory, in which randomness, nonlinearity and geometry are determined by a single scaling parameter, is reported, and it is shown that curvature enhances localization.