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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 308, Pages 9–22
(Mi znsl825)
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This article is cited in 11 scientific papers (total in 12 papers)
On $PC$-ansatz
V. M. Babich St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
The subject of the paper is detailed consideration of known from seventies ansatz:
$$
e^{\operatorname{i}kl(x)}[AD_p(\sqrt{k}e^{-\frac\pi4}m(x))+
k^{-\frac12}e^{\frac\pi4}BD_p^\prime(\sqrt{k}e^{-\frac\pi4}m(x))],
$$
where $A$ and $B$ are series:
$$
A=\sum_{s=0}^\infty\frac{A_s(x)}{(\operatorname{i}k)^s};\quad
B=\sum_{s=0}^\infty\frac{B_s(x)}{(\operatorname{i}k)^s}.
$$
Here $D_p$ are parabolic cylinder functions. Analytical expressions in the first approximation for wave field in the penumbra of the wave reflected by impedance or transparent cone were obtained.
Received: 29.01.2004
Citation:
V. M. Babich, “On $PC$-ansatz”, Mathematical problems in the theory of wave propagation. Part 33, Zap. Nauchn. Sem. POMI, 308, POMI, St. Petersburg, 2004, 9–22; J. Math. Sci. (N. Y.), 132:1 (2006), 2–10
Linking options:
https://www.mathnet.ru/eng/znsl825 https://www.mathnet.ru/eng/znsl/v308/p9
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Abstract page: | 379 | Full-text PDF : | 93 | References: | 91 |
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