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GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. I: Computation of stationary solutions. (English) Zbl 1348.35003

Summary: This paper presents GPELab (Gross-Pitaevskii Equation Laboratory), an advanced easy-to-use and flexible Matlab toolbox for numerically simulating many complex physics situations related to Bose-Einstein condensation. The model equation that GPELab solves is the Gross-Pitaevskii equation. The aim of this first part is to present the physical problems and the robust and accurate numerical schemes that are implemented for computing stationary solutions, to show a few computational examples and to explain how the basic GPELab functions work. Problems that can be solved include: 1d, 2d and 3d situations, general potentials, large classes of local and nonlocal nonlinearities, multi-components problems, and fast rotating gases. The toolbox is developed in such a way that other physics applications that require the numerical solution of general Schrödinger-type equations can be considered.

MSC:

35-04 Software, source code, etc. for problems pertaining to partial differential equations
82-04 Software, source code, etc. for problems pertaining to statistical mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
82-08 Computational methods (statistical mechanics) (MSC2010)
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