非线性准周期薛定谔方程时间分裂投影方法的收敛性分析
Convergence analysis of time-splitting projection method for nonlinear quasiperiodic Schrödinger equation
AI总结：
本文针对非线性准周期薛定谔方程，提出空间投影与时间Strang分裂的数值方法，并证明其空间谱精度与时间二阶收敛性，数值实验验证了理论。
摘要：
本文提出并分析了一种求解具有准周期势的非线性薛定谔方程的高效数值方法，其中在空间上应用投影方法以处理准周期结构，在时间上使用Strang分裂方法。低维准周期函数与高维周期函数之间的空间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，与周期薛定谔系统的传统数值分析相比，许多工具和理论不适用于准周期情形。我们解决了这些问题，证明了空间上的谱精度和时间上的二阶精度。数值实验验证了理论结果。
英文摘要：
This work proposes and analyzes an efficient numerical method for solving the nonlinear Schrödinger 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 Schrödinger 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.
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