平滑Wigner变换的精确方程与波传播的均匀化
Exact equations for smoothed Wigner transforms and homogenization of wave propagation
AI总结：
本文提出平滑Wigner变换并推导其精确方程，用于消除干涉项，以有效模拟波传播问题，并通过薛定谔方程的渐近模型进行数值验证。
摘要：
Wigner变换（WT）已广泛用于各种波传播问题（包括高频极限、非线性波和随机波）的相空间模型构建。众所周知，WT具有反直觉的“干涉项”，这常常使计算变得不切实际。为此，我们提出使用平滑Wigner变换（SWT），并推导出其新的精确方程，涵盖了一大类波传播问题。作为特例，还包括了谱图的方程。通过SWT对干涉项的“驯服”得到了说明，并为薛定谔方程构建了一个渐近模型，且进行了数值验证。
英文摘要：
The Wigner Transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features counterintuitive 'interference terms', which often make computation impractical. In this connection, we propose the use of the smoothed Wigner Transform (SWT), and derive new, exact equations for it, covering a broad class of wave propagation problems. Equations for spectrograms are included as a special case. The 'taming' of the interference terms by the SWT is illustrated, and an asymptotic model for the Schroedinger equation is constructed and numerically verified.
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