This work proposes and analyzes an efficient numerical method for solving the nonlinear Schr\"odinger equation with quasiperiodic potential, where the projection method is applied in space to account for the quasiperiodic structure and the Strang splitting method is used in time.While the transfer between spaces of low-dimensional quasiperiodic and high-dimensional periodic functions and its coupling with the nonlinearity of the operator splitting scheme make the analysis more challenging. Meanwhile, compared to conventional numerical analysis of periodic Schr\"odinger systems, many of the tools and theories are not applicable to the quasiperiodic case. We address these issues to prove the spectral accuracy in space and the second-order accuracy in time. Numerical experiments are performed to substantiate the theoretical findings.

翻译：本文提出并分析了一种用于求解具有准周期势的非线性薛定谔方程的高效数值方法。该方法在空间上采用投影法以处理准周期结构，在时间上采用Strang分裂法。尽管低维准周期函数空间与高维周期函数空间之间的转换，及其与算子分裂格式非线性的耦合，使得分析更具挑战性；同时，与传统的周期薛定谔系统数值分析相比，许多工具和理论不适用于准周期情形。我们针对这些问题进行了分析，证明了该方法在空间上具有谱精度，在时间上具有二阶精度。数值实验验证了理论结果。