High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates

Christophe Besse 1 Guillaume Dujardin 2, 3 Ingrid Lacroix-Violet 4, 3
2 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
4 RAPSODI - Reliable numerical approximations of dissipative systems
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : This article deals with the numerical integration in time of nonlinear Schrödinger 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 Schrödinger 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.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01170888
Contributor : Guillaume Dujardin <>
Submitted on : Monday, January 30, 2017 - 10:03:46 AM
Last modification on : Monday, April 29, 2019 - 3:44:53 PM

Files

high_order_nls_hal.pdf
Files produced by the author(s)

Identifiers

Citation

Christophe Besse, Guillaume Dujardin, Ingrid Lacroix-Violet. High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2017, 55 (3), pp.1387-1411. ⟨10.1137/15M1029047⟩. ⟨hal-01170888v2⟩

Share

Metrics

Record views

1243

Files downloads

292