Geodesic
A complex ray application to calculation of the scalar “non-geometrical” waves
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 20-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper contains a short presentation of the ray method on the complex plane $\mathrm{C}^2$. The calculation of the scalar “non-geometrical” $P^*$-wave is considered as an application of this theory. 
@article{ZNSL_1990_186_a2,
     author = {V. M. Babich},
     title = {A complex ray application to calculation of the scalar {\textquotedblleft}non-geometrical{\textquotedblright} waves},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {20--32},
     year = {1990},
     volume = {186},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a2/}
}
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V. M. Babich. A complex ray application to calculation of the scalar “non-geometrical” waves. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 20-32. http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a2/