发表机构
Clemson University; Zhejiang University of Finance and Economics（克莱姆森大学; 浙江财经大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究旋转非线性薛定谔方程高阶时间分裂，傅里叶拟谱离散化后原方法有问题。为此制定离散线性传播子固定网格可允许性，构造两个可允许传播子，经数值实验验证其有效性，能恢复相应阶数行为。
AI 中文摘要
我们研究了线性部分由拉普拉斯算子和任意三维旋转算子定义的非线性薛定谔方程的鲁棒高阶时间分裂。在傅里叶拟谱离散化后，线性流的连续精确因式分解不一定产生自伴固定网格传播子的方法。对于原始的逐阶段显式精确积分器，我们在局部对数中识别出一个二次偶数项，并表明其可见性取决于状态，因此观察到的时间精度阶数可能取决于初始数据。然后我们为离散线性传播子制定固定网格可允许性，并为任意三维旋转构造两个可允许传播子：一个对称显式精确积分器和一个回文广义剪切传播子。两者都是酉的、一阶一致的、方法自伴的，并且具有奇数局部对数。数值实验验证了预测的缺陷机制，并证明了使用可允许传播子恢复设计的二阶、四阶和六阶行为。
英文摘要
High-order splittings for rotational nonlinear Schrödinger equations may use an exact continuous factorization of the Laplace--rotation flow, but its fixed-grid Fourier realization need not retain the symmetry required by standard symmetric compositions. For the specified realization of the 3D arbitrary-axis explicit exact integrator (EEI), we prove that the complete map has a nonzero quadratic coefficient in its local matrix logarithm for every nonzero rotation on centered even grids. The defect persists under every real consistent composition of the same unrepaired nonlinear sandwich through a positive sum-of-squares factor. We construct two self-adjoint remedies: an adjoint-symmetrized EEI and a palindromic shear alternative. Fourier-tail estimates illustrate the representation mechanism, while complete-map diagnostics and a three-dimensional dipolar benchmark are consistent with the predicted order behavior. An implementation audit separates floating-point coefficient cancellation from the exact-arithmetic symmetry defect.
CommentsReplacement of the original manuscript "Admissible Discrete Linear Propagators for High-Order Time Splittings of Rotational Nonlinear Schrödinger Equations with Arbitrary Three-Dimensional Rotation"
