Two-Dimensional Superfluid Flows in Inhomogeneous Bose-Einstein Condensates
arXiv:1112.5499 · doi:10.1103/PhysRevE.85.016601
Abstract
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.
6 pages, 3 figures, Accepted for publication in Phys. Rev. E
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