Two-Dimensional Superfluid Flows in Inhomogeneous Bose-Einstein   Condensates
  We report a novel 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 Schrodinger 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. 
Zhenya Yan, V. V. Konotop, A. V. Yulin, and W. M. Liu
nlin.SI math-ph math.MP quant-ph