Strong Rates of Convergence of a Splitting Scheme for Schrödinger Equations with Nonlocal Interaction Cubic Nonlinearity and White Noise Dispersion

We analyze a splitting integrator for the time discretization of Schrödinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. prove that this has order convergence one in $p$th mean sense, any $p\geq1$ some Sobolev spaces. schemes preserves $L^2$-norm, which is crucial property proof strong result. Finally, numerical experiments illustrate performance proposed scheme.