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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 1961, Volume 1, Number 1, Pages 90–104 (Mi zvmmf8026)  
The asymptotic expansion of Green's function for the diffraction of short waves by a paraboloid of revolution (axisymmetric case)

V. I. Ivanov

Moscow
Full-text PDF (1257 kB)
Abstract: Asymptotic expansions of Green's function are found which are equally valid in semi-shadow and shadow regions. Green's function is constructed for a paraboloid of revolution.
The stationary phase method is used in the illuminated region, and gives the formulae of geomerical acoustics. It enables the principal integration interval in the expressions for the currents on the surface of the paraboloid to be determined. In the semi-shadow and shadow regions Fok type expansions must be used.
Asymptotic expansions are found for the diffraction field in space.
The appendix discusses asymptotic expansions of Whittaker's degenerate function.
Received: 14.10.1960
English version:
USSR Computational Mathematics and Mathematical Physics, 1961, Volume 1, Issue 1, Pages 97–113
DOI: https://doi.org/10.1016/0041-5553(62)90008-3
Bibliographic databases:
Language: Russian
Citation: V. I. Ivanov, “The asymptotic expansion of Green's function for the diffraction of short waves by a paraboloid of revolution (axisymmetric case)”, Zh. Vychisl. Mat. Mat. Fiz., 1:1 (1961), 90–104; U.S.S.R. Comput. Math. Math. Phys., 1:1 (1961), 97–113
Citation in format AMSBIB
\Bibitem{Iva61}
\by V.~I.~Ivanov
\paper The asymptotic expansion of Green's function for the diffraction of short waves by a paraboloid of revolution (axisymmetric case)
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1961
\vol 1
\issue 1
\pages 90--104
\mathnet{http://mi.mathnet.ru/zvmmf8026}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=0135833}
\zmath{https://zbmath.org/?q=an:0122.21801}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1961
\vol 1
\issue 1
\pages 97--113
\crossref{https://doi.org/10.1016/0041-5553(62)90008-3}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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