Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation

The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions d less than or equal to 2, and we propose the appropriate low-dimensional modifications. For d=1 we analyze density profiles in confining potentials, superfluid properties, solitons, and self-similar solutions.