Geodesic
Local degeneration of waves in a thin waveguide
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 138-148

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A thin, curved waveguide of variable width with an impedance condition on one of the walls is considered. Local degeneration of normal waves is studied. Coefficients for the transformation of waves as they pass through points of local degeneration are found. 
@article{ZNSL_1978_78_a10,
     author = {I. A. Molotkov and A. S. Starkov},
     title = {Local degeneration of waves in a thin waveguide},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {138--148},
     publisher = {mathdoc},
     volume = {78},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a10/}
}
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I. A. Molotkov; A. S. Starkov. Local degeneration of waves in a thin waveguide. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 138-148. http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a10/