High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates
This work provides improved numerical methods for simulating rotating Bose-Einstein condensates, which is important for computational physics but represents an incremental advance over existing exponential integrator techniques.
The authors developed high-order exponential integrators for nonlinear Schrödinger equations, specifically for rotating Bose-Einstein condensates, and demonstrated through numerical experiments that these methods achieve better accuracy and efficiency compared to classical split-step methods.
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.