High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates

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.