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)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 MEPHYSTO - Quantitative methods for stochastic models in physics
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 RAPSODI - Reliable numerical approximations of dissipative systems

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.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Christophe Besse, Guillaume Dujardin, Ingrid Lacroix-Violet. High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates. 2015. ⟨hal-01170888v1⟩