Geodesic
Radiation of a normal wave in case of passing the critical section of a wave-guide of variable thickness
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 17, Tome 165 (1987), pp. 166-176 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of wave propagation in slowly tapered waveguide is investigated. Usual asymptotic expansion break down in critical width region. The field in transition region described in terms of Airy function if two media boundary is a straight line. It is shown that the curvature of boundary leads to the more complicated expansion of dock's type. 
@article{ZNSL_1987_165_a15,
     author = {A. S. Starkov},
     title = {Radiation of a normal wave in case of passing the critical section of a wave-guide of variable thickness},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {166--176},
     year = {1987},
     volume = {165},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_165_a15/}
}
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A. S. Starkov. Radiation of a normal wave in case of passing the critical section of a wave-guide of variable thickness. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 17, Tome 165 (1987), pp. 166-176. http://geodesic.mathdoc.fr/item/ZNSL_1987_165_a15/