Section: New Results

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

In a recent work with C. Besse and I. Violet [6], Guillaume Dujardin has proposed and analyzed new methods for the time integration of the nonlinear Schrödinger equation in the context of rotating Bose–Einstein condensates. In particular, he has proposed a systematic way to design high-order in time implicit exponential methods, given sufficient conditions to ensure mass preservation by the methods and proved high order in several physically relevant situations. He has compared those methods to several other popular methods from the literature and provided several numerical experiments.