title: Stationary solutions for the 2+1 nonlinear Schrödinger equation modeling Bose-Einstein condensates in radial potentials.
abstract: Stationary solutions for the 2+1 cubic nonlinear Schrödinger equation modeling Bose-Einstein condensates (BEC) in a small potential are obtained via a form of perturbation. In particular, perturbations due to small potentials which either confine or repel the BECs are studied, and under arbitrary piecewise continuous potentials, we obtain the general representation for the perturbation theory of radial BEC solutions. Numerical results are also provided for regimes where perturbative results break down (i.e., the large-potential regime). Both repulsive and attractive BECs are considered under this framework. Solutions for many specific confining potentials of physical relevance to experiments on BECs are provided in order to demonstrate the approach. We make several observations regarding the influence of the particular small potentials on the behavior of the BECs.
authors.affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816-1364, USA.
authors.forename: Kristina
authors.initials: K
authors.lastname: Mallory
authors.affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816-1364, USA.
authors.forename: Robert A
authors.initials: RA
authors.lastname: Van Gorder
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D011789:Quantum Theory