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arXiv · 1507.00550

High order exponential integrators for nonlinear Schr\"odinger equations with application to rotating Bose-Einstein condensates

Christophe Besse·Guillaume Dujardin·Ingrid Lacroix-Violet
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Abstract

This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the rotation term disappears and they obtain as a result a nonautonomous nonlinear Schr\"odinger equation. They consider exponential integrators such as exponential Runge--Kutta methods and Lawson methods. They provide an analysis of the order of convergence and some preservation properties of these methods in a simplified setting and they supplement their results with numerical experiments with realistic physical parameters. Moreover, they compare these methods with the classical split-step methods applied to the same problem.

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Christophe Besse, Guillaume Dujardin, Ingrid Lacroix-Violet. 2015-07-02. High order exponential integrators for nonlinear Schr\"odinger equations with application to rotating Bose-Einstein condensates. https://arxiv.org/abs/1507.00550

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