We propose a nodal discontinuous Galerkin method for solving the nonlinear Riesz space fractional Schrödinger equation and the strongly coupled nonlinear Riesz space fractional Schrödinger equations. These problems have been expressed as a system of low order dif- ferential/integral equations. Moreover, we prove, for both problems, L 2 stability and opti- mal order of convergence O (h N+1 ) , where h is space step size and N is polynomial degree. Finally, the performed numerical experiments confirm the optimal order of convergence