非线性薛定谔方程的开放边界
Open Boundaries for the Nonlinear Schrodinger Equation
AI总结：
提出时间相关相空间滤波器（TDPSF）算法，通过周期性分解相干态并删除外向态，解决非线性薛定谔方程在周期边界下的反射波问题，并提供数值结果和严格误差估计。
摘要：
我们提出了一种新算法——时间相关相空间滤波器（TDPSF），用于求解时间相关的非线性薛定谔方程（NLS）。该算法包括在具有周期边界条件的盒子上求解NLS（通过任意算法）。周期性地在时间上，我们将解分解为一族相干态。外向的相干态被删除，而非外向的则保留，从而减少反射（包裹）波的问题。给出了数值结果，并描述了严格的误差估计。TDPSF与谱方法兼容，用于求解内部问题。TDPSF还能优雅地失效，即当结果不正确时算法会通知用户。据我们所知，没有其他方法具有这种能力。
英文摘要：
We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF) which is used to solve time dependent Nonlinear Schrodinger Equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those which are not are kept, reducing the problem of reflected (wrapped) waves. Numerical results are given, and rigorous error estimates are described. The TDPSF is compatible with spectral methods for solving the interior problem. The TDPSF also fails gracefully, in the sense that the algorithm notifies the user when the result is incorrect. We are aware of no other method with this capability.
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