Geodesic
Diffraction of plane wave by a~transparent wedge: Sommerfeld--Malyuzhinets approach
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 37, Tome 354 (2008), pp. 157-172

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We consider a time-harmonic diffraction of a plane wave by a transparent wedge of an arbitrary opening by the Sommerfeld–Malyuzhinets approach, see, e.g., [1]. The wave propagation velocity inside the wedge and outside are equal. An explicit solution is presented, which is studied asymptotically as $kr\to\infty$ and $kr\to0$. Bibl. – 4 titles, fig. – 6. 
@article{ZNSL_2008_354_a7,
     author = {A. A. Matskovskii},
     title = {Diffraction of plane wave by a~transparent wedge: {Sommerfeld--Malyuzhinets} approach},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {157--172},
     publisher = {mathdoc},
     volume = {354},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_354_a7/}
}
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A. A. Matskovskii. Diffraction of plane wave by a~transparent wedge: Sommerfeld--Malyuzhinets approach. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 37, Tome 354 (2008), pp. 157-172. http://geodesic.mathdoc.fr/item/ZNSL_2008_354_a7/