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Friedlander–Keller ray expansions and scalar wave reflection at canonically perturbed boundaries

Published online by Cambridge University Press:  04 January 2018

R.H. TEW*
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK email: richard.tew@nottingham.ac.uk

Abstract

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).

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Papers
Copyright
Copyright © Cambridge University Press 2018 

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References

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