Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation

Abstract

In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schrödinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method. By introducing an auxiliary variable, we first transform the original model into an equivalent system which admits both mass and modified energy. Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of massand energy-conserving time-discrete schemes. Numerical experiments are addressed to demonstrate the accuracy and effectiveness of the newly proposed schemes.