Geodesic
Scattering amplitudes in a~neighborhood of the limit rays in shortwave diffraction problems of a~plane wave by elongated bodies of revolution
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 232-253

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In the paper we consider diffraction problems of a plane wave by smooth, convex and elongated bodies of revolution in the framework of short wave approximation (axially symmetric cases), calculate the scattering amplitudes in the direction of limit rays and investigate the influence of prolateness of the scatterers on the amplitudes behaviour. Mathematical technique of our approach is based on the Green's formulas in exterior of the scatterers and numerical calculations of the wave field current in the boundary layers in a vicinity of the light-shadow zone. It emerged that the prolateness of the axially symmetric bodies relatively weakly affects the scattering amplitudes short wave asymptotics. The main contribution to the amplitudes is made by the solution of the 2D diffraction problem by a convex, smooth curve in the cross section of the scatterers by a plane containing the rotation axis. 
@article{ZNSL_2017_461_a12,
     author = {M. M. Popov and N. M. Semtchenok},
     title = {Scattering amplitudes in a~neighborhood of the limit rays in shortwave diffraction problems of a~plane wave by  elongated bodies of revolution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {232--253},
     publisher = {mathdoc},
     volume = {461},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a12/}
}
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M. M. Popov; N. M. Semtchenok. Scattering amplitudes in a~neighborhood of the limit rays in shortwave diffraction problems of a~plane wave by  elongated bodies of revolution. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 232-253. http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a12/