TY - JOUR

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

AU - Kucherenko, V. V.

PY - 1968/1/1

Y1 - 1968/1/1

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.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=49949129238&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=49949129238&origin=inward

U2 - 10.1016/0041-5553(68)90169-9

DO - 10.1016/0041-5553(68)90169-9

M3 - Article

SP - 294

EP - 302

JO - USSR Computational Mathematics and Mathematical Physics

JF - USSR Computational Mathematics and Mathematical Physics

SN - 0041-5553

ER -