Unidimensional reduction of the 3D Gross-Pitaevskii equation with two- and three-body interactions
arXiv:1012.1839 · doi:10.1103/PhysRevE.83.036604
Abstract
We deal with the three-dimensional Gross-Pitaevskii equation, which is used to describe a cloud of dilute bosonic atoms that interact under competing two- and three-body scattering potentials. We study the case where the cloud of atoms is strongly confined in two spatial dimensions, allowing us to build an unidimensional nonlinear equation, controlled by the nonlinearities and the confining potentials that trap the system along the longitudinal coordinate. We focus attention on specific limits, dictated by the cubic and quintic coefficients, and we implement numerical simulations to help us to quantify the validity of the procedure.
6 pages, 4 figures; version to appear in PRE
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- C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
- Quasi-one-dimensional approximation for Bose-Einstein condensates transversely trapped by a funnel potential
- Generic transverse stability of kink structures in atomic and optical nonlinear media with competing attractive and repulsive interactions
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