In the paper, we aim to develop a class of high-order structure-preserving algorithms, which are built upon the idea of the newly introduced scalar auxiliary variable approach, for the multi-dimensional space fractional nonlinear Schrödinger equation. First, we reformulate the equation as an infinite-dimension canonical Hamiltonian system, and obtain an equivalent system with a modified energy conservation law by using the scalar auxiliary variable approach. Then, the new system is discretized by Gauss collocation methods to arrive at semi-discrete conservative systems. Subsequently, the Fourier pseudo-spectral method is applied for semi-discrete systems to obtain high-order fully-discrete schemes, which can both preserve the mass and the modified energy exactly in discrete scene. Finally, numerical experiments are provided to demonstrate the conservation and accuracy of the proposed schemes.

本文旨在针对多维空间分数阶非线性Schrödinger方程，开发一类基于新引入的标量辅助变量方法的思想的高阶结构保持算法。首先，我们将该方程式重新表述为无穷规范的哈密顿系统，并使用标量辅助变量法获得具有修改后的节能规律的等效系统。然后，通过高斯配置方法将新系统离散化，得到半离散保守系统。随后，将傅里叶伪谱方法应用于半离散系统以获得高阶全离散方案，该方案既可以在离散场景中精确地保留质量，又可以保留修改后的能量。最后，