The short-wave asymptotic behaviour of Green's function for the n-dimensional wave equation in an inhomogeneous medium

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Abstract

IN the present paper the asymptotic behaviour of Green's function is studied for the wave equation [Δ + k2n2(x)]G = δ(x - x0), G = O( 1 |x| (N - 1> 2), ∂G ∂|x| + ik √EG = o( 1 |x| (N - 1) 2), (1) x = (x1, ..., xN), E = lim |x|→+∞ n2(x), n2 = E - V(x) > 0 in an N-dimensional space as k → + ∞. An asymptotic function will be constructed subject to the following conditions on the function n2(x). © 1970.
Original languageAmerican English
Pages (from-to)294-302
Number of pages263
JournalUSSR Computational Mathematics and Mathematical Physics
DOIs
StatePublished - 1 Jan 1968

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Green function
wave equation
Wave equations
Green's function

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title = "The short-wave asymptotic behaviour of Green's function for the n-dimensional wave equation in an inhomogeneous medium",
abstract = "IN the present paper the asymptotic behaviour of Green's function is studied for the wave equation [Δ + k2n2(x)]G = δ(x - x0), G = O( 1 |x| (N - 1> 2), ∂G ∂|x| + ik √EG = o( 1 |x| (N - 1) 2), (1) x = (x1, ..., xN), E = lim |x|→+∞ n2(x), n2 = E - V(x) > 0 in an N-dimensional space as k → + ∞. An asymptotic function will be constructed subject to the following conditions on the function n2(x). {\circledC} 1970.",
author = "Kucherenko, {V. V.}",
year = "1968",
month = "1",
day = "1",
doi = "10.1016/0041-5553(68)90169-9",
language = "American English",
pages = "294--302",
journal = "USSR Computational Mathematics and Mathematical Physics",
issn = "0041-5553",
publisher = "Pergamon Press Ltd.",

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T1 - The short-wave asymptotic behaviour of Green's function for the n-dimensional wave equation in an inhomogeneous medium

AU - Kucherenko, V. V.

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N2 - IN the present paper the asymptotic behaviour of Green's function is studied for the wave equation [Δ + k2n2(x)]G = δ(x - x0), G = O( 1 |x| (N - 1> 2), ∂G ∂|x| + ik √EG = o( 1 |x| (N - 1) 2), (1) x = (x1, ..., xN), E = lim |x|→+∞ n2(x), n2 = E - V(x) > 0 in an N-dimensional space as k → + ∞. An asymptotic function will be constructed subject to the following conditions on the function n2(x). © 1970.

AB - IN the present paper the asymptotic behaviour of Green's function is studied for the wave equation [Δ + k2n2(x)]G = δ(x - x0), G = O( 1 |x| (N - 1> 2), ∂G ∂|x| + ik √EG = o( 1 |x| (N - 1) 2), (1) x = (x1, ..., xN), E = lim |x|→+∞ n2(x), n2 = E - V(x) > 0 in an N-dimensional space as k → + ∞. An asymptotic function will be constructed subject to the following conditions on the function n2(x). © 1970.

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