Geodesic
``Separation of variables'' in the model problems of the diffraction theory. Formal scheme
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 124-139

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Parabolic equation describes propagation of the localized waves along the boundary with peculiarities. We present here some reformulation of the “separation of variables”, which gives the possibility to obtain rich set of solutions of the corresponding boundary problems. 
@article{ZNSL_2018_471_a8,
     author = {A. Ya. Kazakov},
     title = {``Separation of variables'' in the model problems of the diffraction theory. {Formal} scheme},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {124--139},
     publisher = {mathdoc},
     volume = {471},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a8/}
}
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A. Ya. Kazakov. ``Separation of variables'' in the model problems of the diffraction theory. Formal scheme. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 124-139. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a8/