Before revision: In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schr\"odinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method.
After revision: In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods are developed for the nonlinear Schr\"odinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method.