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 | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/qam/652051

Article copyright:
© Copyright 1982
American Mathematical Society