A Structure-Preserving Discretization of Nonlinear Schrödinger Equation

Abstract

This paper studies the geometric structure of nonlinear Schrödinger equation and from the viewpoint of preserving structure a kind of fully discrete schemes is presented for the numerical simulation of this important equation in quantum. It has been shown by theoretical anaysis and numerical experiments that such discrete schemes are quite satisfactory in keeping the desirable conservation properties and for simulating the long-time behaviour.