Geodesic
On an integral equation in the problem of the plane wave diffraction by a~circular transparent cone
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 33, Tome 308 (2004), pp. 101-123

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The problem of diffraction by a transparent convex cone is studied. The uniqueness theorem is proven in the problem of diffraction for the illumination by a compact source. For the circular cone the solution is obtained in the form of the Kontorovich–Lebedev integrals and of the Fourier series expansions. A singular integral equation is deduced for the Fourier coefficients and its reqularization is performed. 
@article{ZNSL_2004_308_a6,
     author = {M. A. Lyalinov},
     title = {On an integral equation in the problem of the plane wave diffraction by a~circular transparent cone},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {101--123},
     publisher = {mathdoc},
     volume = {308},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_308_a6/}
}
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M. A. Lyalinov. On an integral equation in the problem of the plane wave diffraction by a~circular transparent cone. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 33, Tome 308 (2004), pp. 101-123. http://geodesic.mathdoc.fr/item/ZNSL_2004_308_a6/