Geodesic
Asymptotics of waves diffracted by a cone and diffraction series on a sphere
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 234-258 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Diffraction of a plane harmonic scalar wave by a cone with ideal boundary condition is studied. A flat cone or a circular cone is chosen as a scatterer. It is known that the diffarcted field contains different components: a spherical wave, geometrically reflected wave, multiply diffracted cylindrical waves (for a flat cone), creepind waves (for a circular cone). The main task of the paper is to find a uniform asymptotics of all wave components. This problem is solved by using an integral representation proposed in the works by V. M. Babich and V. P. Smyshlyaev. This representaition uses a Green's function of the problem on a unit sphere with a cut. This Green's function can be presented in the form of diffraction series. It is shown that different terms of the series correspond to different wave components of the conical diffraction problem. A simple formula connecting the leading terms of the diffraction series for the spherical Green's function with the leading terms of different wave components of the conical problem is derived. Some important particular cases are studied. 
@article{ZNSL_2011_393_a16,
     author = {A. V. Shanin},
     title = {Asymptotics of waves diffracted by a~cone and diffraction series on a~sphere},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {234--258},
     year = {2011},
     volume = {393},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a16/}
}
TY  - JOUR
AU  - A. V. Shanin
TI  - Asymptotics of waves diffracted by a cone and diffraction series on a sphere
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 234
EP  - 258
VL  - 393
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a16/
LA  - ru
ID  - ZNSL_2011_393_a16
ER  - 
%0 Journal Article
%A A. V. Shanin
%T Asymptotics of waves diffracted by a cone and diffraction series on a sphere
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 234-258
%V 393
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a16/
%G ru
%F ZNSL_2011_393_a16
A. V. Shanin. Asymptotics of waves diffracted by a cone and diffraction series on a sphere. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 234-258. http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a16/

[1] V. M. Babich, D. B. Dement'ev, B. A. Samokish, V. P. Smyshlyaev, “On evaluation of the diffraction coefficient for arbitrary “nonsingular” directions of a smooth convex cone”, SIAM J. Appl. Math., 60:2 (2000), 536–573 | DOI | MR | Zbl

[2] V. A. Borovikov, Difraktsiya na mnogougolnikakh i mnogogrannikakh, Nauka, M., 1966 | MR

[3] V. M. Babich, “O PTs-anzatse”, Zap. nauchn. semin. POMI, 308, 2004, 9–22 | MR | Zbl

[4] A. Popov, A. Ladyzhensky, S. Khoziosky, “Uniform asymptotics of the wave diffracted by a cone of arbitrary cross-section”, Russ. J. Math. Phys., 16:2 (2009), 296–299 | DOI | MR | Zbl

[5] I. V. Andronov, “Difraktsiya na nekotorykh silno vytyanutykh telakh vrascheniya”, Akusticheskii zhurnal (to appear)