Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A geometric-optical series and a WKB paradox


Author: Samuel H. Gray
Journal: Quart. Appl. Math. 40 (1982), 73-81
MSC: Primary 34E05; Secondary 58G15, 78A45
DOI: https://doi.org/10.1090/qam/652051
MathSciNet review: 652051
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Abstract: We discuss a solution of the one-dimensional reduced wave equation with non-constant velocity. We show that, for sufficiently small total velocity variations, this solution is exact. Furthermore, it lends itself to (high-frequency) asymptotic analysis and to elementary numerical analysis in a natural way. For reflected waves, we show that asymptotically small reflection implies numerically small reflection, thus resolving a paradox of classical WKB theory.


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DOI: https://doi.org/10.1090/qam/652051
Article copyright: © Copyright 1982 American Mathematical Society


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