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In this paper, we consider the numerical solution of a nonlinear Schrodingerequation with spatial random potential. The randomly shifted quasi-Monte Carlo(QMC) lattice rule combined with the time-splitting pseudospectraldiscretization is applied and analyzed. The nonlinearity in the equationinduces difficulties in estimating the regularity of the solution in randomspace. By the technique of weighted Sobolev space, we identify the possibleweights and show the existence of QMC that converges optimally at thealmost-linear rate without dependence on dimensions. The full error estimate ofthe scheme is established. We present numerical results to verify the accuracyand investigate the wave propagation.

Error estimate of a quasi-Monte Carlo time-splitting pseudospectral method for nonlinear Schrodinger equation with random potentials