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A GEOMETRIC-OPTICAL SERIES AND A WKB PARADOX
SAMUEL H. GRAY
Quarterly of Applied Mathematics
Vol. 40, No. 1 (April 1982), pp. 73-81
Published by: Brown University
Stable URL: http://www.jstor.org/stable/43637123
Page Count: 9
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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.
Quarterly of Applied Mathematics © 1982 Brown University