Geodesic
Excitation of normal modes of a weakly inhomogeneous waveguide by a point source
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 174-178 
N. A. Razumovskii. Excitation of normal modes of a weakly inhomogeneous waveguide by a point source. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 174-178. http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a15/
@article{ZNSL_1984_140_a15,
     author = {N. A. Razumovskii},
     title = {Excitation of normal modes of a~weakly inhomogeneous waveguide by a~point source},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--178},
     year = {1984},
     volume = {140},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a15/}
}
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An asymptotic expansion of the Green function is constructed for a weakly inhomogeneous waveguide. Matching of asymptotic expansions is used.