Geodesic
Shortwave grazing scattering of a plane wave on a smooth periodic boundary. II. Diffraction on an infinite periodic boundary
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 60-86

Voir la notice de l'article provenant de la source Math-Net.Ru

Scattering problem of a plane wave on a smooth periodic surface in the case of small grazing angle and shortwave approximation is considered (period and radius of curvature of the boundary are supposed to be large in compare with wave length). The solution of the problem is constructed as an infinite sum of multiple diffracted fields in a vicinity of the reflecting boundary (Fock's region and penumbra). Series of the multiple diffracted fields can be summed by means of a certain Winer–Hopf–Fock integral equation. Closed formulas for two leading terms of the shortwave aproximation of the solution is obtained. 
@article{ZNSL_1988_173_a5,
     author = {V. V. Zalipaev and M. M. Popov},
     title = {Shortwave grazing scattering of a plane wave on a smooth periodic boundary. {II.} {Diffraction} on an infinite periodic boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--86},
     publisher = {mathdoc},
     volume = {173},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a5/}
}
TY  - JOUR
AU  - V. V. Zalipaev
AU  - M. M. Popov
TI  - Shortwave grazing scattering of a plane wave on a smooth periodic boundary. II. Diffraction on an infinite periodic boundary
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1988
SP  - 60
EP  - 86
VL  - 173
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a5/
LA  - ru
ID  - ZNSL_1988_173_a5
ER  - 
%0 Journal Article
%A V. V. Zalipaev
%A M. M. Popov
%T Shortwave grazing scattering of a plane wave on a smooth periodic boundary. II. Diffraction on an infinite periodic boundary
%J Zapiski Nauchnykh Seminarov POMI
%D 1988
%P 60-86
%V 173
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a5/
%G ru
%F ZNSL_1988_173_a5
V. V. Zalipaev; M. M. Popov. Shortwave grazing scattering of a plane wave on a smooth periodic boundary. II. Diffraction on an infinite periodic boundary. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 60-86. http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a5/