Abstract:
A function $V$ having Gaussian beam asymptotic (the frequency $\omega\to+\infty$) is obtained. The expression $(\Delta+\frac{\omega^2}{c^2(x)})V$ is exponentialy small in the the neighbourhood of axial ray of Gaussian beam. The velocity $c(x)$ is analitical.
Citation:
V. M. Babich, “The construction of Gaussian beams satisfying to the wave equation with exponential exactness”, Mathematical problems in the theory of wave propagation. Part 22, Zap. Nauchn. Sem. POMI, 203, Nauka, St. Petersburg, 1992, 17–20; J. Math. Sci., 79:4 (1996), 1169–1171
\Bibitem{Bab92}
\by V.~M.~Babich
\paper The construction of Gaussian beams satisfying to the wave equation with exponential exactness
\inbook Mathematical problems in the theory of wave propagation. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 1992
\vol 203
\pages 17--20
\publ Nauka
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5769}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1193676}
\zmath{https://zbmath.org/?q=an:0856.35032}
\transl
\jour J. Math. Sci.
\yr 1996
\vol 79
\issue 4
\pages 1169--1171
\crossref{https://doi.org/10.1007/BF02362882}
Linking options:
https://www.mathnet.ru/eng/znsl5769
https://www.mathnet.ru/eng/znsl/v203/p17
This publication is cited in the following 1 articles:
V. P. Palamodov, “New approaches to inverse scattering”, Russian Math. Surveys, 71:3 (2016), 513–537
Citation in format AMSBIB
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