Friedlander–Keller ray expansions and scalar wave reflection at canonically perturbed boundaries
Friedlander–Keller ray expansions and scalar wave reflection at canonically perturbed boundaries
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正则扰动边界处的弗里德兰德-凯勒射线展开和标量波反射
DOI：
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发表时间：
2018
影响因子：
1.9
通讯作者：
R. Tew
中科院分区：
文献类型：
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作者：
R. Tew
本文研究了波数为k（k − 1）的高频单色线性波从光滑边界上的反射，这些光滑边界是O（k−1/2）扰动，远离指定的近平面边界或给定的一般曲率为O（1）的光滑二维曲线。对于每一类扰动边界，我们将分别考虑平面波和柱面波的入射，以及每种入射场的一般振幅分布。这种界面扰动缩放是规范的意义上说，射线的方法需要修改的标准WKBJ的“射线anximity”，这反过来又导致了一个领先的顺序振幅（或“运输”）方程，其中包括一个额外的长期缺席的标准应用的几何衍射理论。这个额外的项对于这种定标是唯一的，并且所需的上述修改是首先由F提出的广义类型的射线展开的应用。G. Friedlander和J. B. Keller（1955）Pure Appl.Math.6，387-394）。
This paper concerns the reflection of high-frequency, monochromatic linear waves of wavenumber k(≫ 1) from smooth boundaries which are O(k−1/2) perturbations away from either a specified near-planar boundary or else from a given smooth, two-dimensional curve of general O(1) curvature. For each class of perturbed boundary, we will consider separately plane and cylindrical wave incidence, with general amplitude profiles of each type of incident field. This interfacial perturbation scaling is canonical in the sense that a ray approach requires a modification to the standard WKBJ ‘ray ansatz’ which, in turn, leads to a leading-order amplitude (or ‘transport’) equation which includes an extra term absent in a standard application of the geometrical theory of diffraction. This extra term is unique to this scaling, and the afore-mentioned modification that is required is an application of a generalised type of ray expansion first posed by F. G. Friedlander and J. B. Keller (1955 Commun. Pure Appl. Math. 6, 387–394).