In this paper, we develop a class of explicit energy-preserving Runge-Kutta schemes for solving the nonlinear Schrödinger equation based on the projection technique and the exponential time differencing method. First, we reformulate the equation to an equivalent system that possesses new quadratic energy via introducing an auxiliary variable. Then, we construct a family of fully discrete exponential time differencing schemes which have better stability by using the Runge-Kutta method and the Fourier-pseudo spectral method to approximate the system in time and space, respectively. Subsequently, energy-preserving schemes are derived by combining the proposed explicit schemes and the projection technique, and the stability result is given. Finally, extensive numerical examples are presented to confirm the constructed schemes have high accuracy, energy-preserving and effectiveness in long time simulation.

在本文中，我们开发了一类基于投影技术和指数时间差分法求解非线性薛定谔方程的显式保能龙格-库塔格式。首先，我们通过引入辅助变量将方程重新构造为具有新二次能量的等效系统。然后，我们分别使用Runge-Kutta方法和Fourier-pseudo Spectrum方法在时间和空间上逼近系统，构造了一系列具有更好稳定性的完全离散指数时间差分方案。随后，将所提出的显式方案与投影技术相结合，推导出了能量保持方案，并给出了稳定性结果。最后，给出了大量的数值例子，以确认所构建的方案具有较高的准确性，