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 $d\le 2$, and we propose the appropriate low-dimensional modifications, which have a universal form. For $d=1\mathrm{}$ we analyze density profiles in confining potentials, superfluid properties, solitons, and self-similar solutions.