Geodesic
High-frequency asymptotics of solutions of the Helmholtz equation in a region of caustic shadow. II
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 17, Tome 165 (1987), pp. 182-188 
Z. A. Yanson. High-frequency asymptotics of solutions of the Helmholtz equation in a region of caustic shadow. II. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 17, Tome 165 (1987), pp. 182-188. http://geodesic.mathdoc.fr/item/ZNSL_1987_165_a17/
@article{ZNSL_1987_165_a17,
     author = {Z. A. Yanson},
     title = {High-frequency asymptotics of solutions of the {Helmholtz} equation in a region of caustic {shadow.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {182--188},
     year = {1987},
     volume = {165},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_165_a17/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Results of the first part of this work for the analytic index of refraction $n(x,z)$ where the complex eikonal in the shadow region behind a caustic is found by the method of characteristics in the two-dimensional complex space $\mathbb{C}^2$, are applied for $n(x,z)$ of finite smoothness. The use of the quadratic approximation for$n(x,z)$ allows one to obtain the zeroth approximation of the asymptotic limit of the wave field behind a caustic in the boundary layer of width $O(\omega^{-2/3})$.