Geodesic
Edge Green's functions on a multi-sheet surface. Asymptotics of solutions of
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 233-256

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The problems of of diffraction by a strip or a set of strips with ideal boundary conditions, as well as some other problems, can be reduced to the scattering problems on multi-sheet surfaces by applying the method of reflections. Further reducing of these problems can be achieved by applying the embedding formulae. As the result, the solution of the problem with a plane wave incidence becomes expressed through edge Green's functions, i.e. the fields excited by dipole sources localized in the branch points of the surface. The paper is dedicated to finding the edge Green's functions. Two systems of differential equations are derived to solve this problem, namely the coordinate and spectral equations. The proprties of solutions for those systems are studied. 
@article{ZNSL_2007_342_a11,
     author = {A. V. Shanin},
     title = {Edge {Green's} functions on a multi-sheet surface. {Asymptotics} of solutions of},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {233--256},
     publisher = {mathdoc},
     volume = {342},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_342_a11/}
}
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A. V. Shanin. Edge Green's functions on a multi-sheet surface. Asymptotics of solutions of. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 233-256. http://geodesic.mathdoc.fr/item/ZNSL_2007_342_a11/