title: Two-dimensional superfluid flows in inhomogeneous Bose-Einstein condensates.
abstract: We report an algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent superfluid flows in inhomogeneous Bose-Einstein condensates. The method is based on the combination of the similarity reduction of the two-dimensional Gross-Pitaevskii equation to the one-dimensional nonlinear Schrödinger equation, the latter allowing for exact solutions, with the conformal mapping of the given domain, where the flow is considered, to a half space. The stability of the obtained flows is addressed. A number of stable and physically relevant examples are described.
authors.affiliation: Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China. zyyan_math@yahoo.com
authors.forename: Zhenya
authors.initials: Z
authors.lastname: Yan
authors.forename: V V
authors.initials: VV
authors.lastname: Konotop
authors.forename: A V
authors.initials: AV
authors.lastname: Yulin
authors.forename: W M
authors.initials: WM
authors.lastname: Liu