Geodesic
Diffraction of wave by cylindrical surface with discontinuous impedance
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 23, Tome 210 (1994), pp. 164-174 Cet article a éte moissonné depuis la source Math-Net.Ru

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A leading term of asymptotics is developed for the two-dimensional problem of diffraction of a plane wave by a smooth cylinder with discontinuous impedance. The key domain in the vicinity of light-shadow boundary (Fock region) is considered. It is supposed that the point of the surface impedance jump is placed near the light-shadow boundary. This leads to the intersection of transition regions caused by the discontinuity and the light-shadow terminator respectively. The leading terms include new type Fock integrals beside the standard ones. The asymptotics is simplified in the penumbral, lighted and shadowed regions. Asymptotic evaluation of the integrals leads to the description of the waves of new type which are absent for continuous impedance. Bibliography: 7 titles. 
@article{ZNSL_1994_210_a14,
     author = {M. A. Lyalinov},
     title = {Diffraction of wave by cylindrical surface with discontinuous impedance},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {164--174},
     year = {1994},
     volume = {210},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_210_a14/}
}
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M. A. Lyalinov. Diffraction of wave by cylindrical surface with discontinuous impedance. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 23, Tome 210 (1994), pp. 164-174. http://geodesic.mathdoc.fr/item/ZNSL_1994_210_a14/