High order exponential integrators for nonlinear Schr\"odinger equations with application to rotating Bose-Einstein condensates
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.
Cite
@article{arxiv.1507.00550,
title = {High order exponential integrators for nonlinear Schr\"odinger equations with application to rotating Bose-Einstein condensates},
author = {Christophe Besse and Guillaume Dujardin and Ingrid Lacroix-Violet},
journal= {arXiv preprint arXiv:1507.00550},
year = {2017}
}