Geodesic
Physical pattern of wave emission in a wedge-shaped region: Generalization of the transverse diffusion method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1576-1590

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An analysis of the rigorous solution to the problem of waves emitted by sources arbitrarily distributed along a wedge face is used to propose a generalization of the Malyuzhinets heuristic transverse diffusion method. Mathematically, the problem is reduced to the numerical solution of a parabolic equation in ray coordinates with prescribed discontinuities on the boundaries of the shadow zone of partial plane waves or with a distributed right-hand side. The physical concept of the phase synchronism of emitted and diffracted waves is stated. 
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     author = {S. A. Zapunidi and A. V. Popov},
     title = {Physical pattern of wave emission in a~wedge-shaped region: {Generalization} of the transverse diffusion method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1576--1590},
     publisher = {mathdoc},
     volume = {47},
     number = {9},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a11/}
}
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S. A. Zapunidi; A. V. Popov. Physical pattern of wave emission in a wedge-shaped region: Generalization of the transverse diffusion method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1576-1590. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a11/