Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-12-23
Phys. Rev. E 85, 016601 (2012)
Nonlinear Sciences
Exactly Solvable and Integrable Systems
6 pages, 3 figures, Accepted for publication in Phys. Rev. E
Scientific paper
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.
Konotop Vladimir V.
Liu Wei-Min
Yan Zhenya
Yulin Alexander V.
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