Geodesic
Parabolic equation and Pearcey-type integral for a transmitted wavefield
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 29, Tome 264 (2000), pp. 140-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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High-frequence wavefield of a point source situated near an interface of two homogeneous media and placed in the faster medium is considered. We are interested in description of a vicinity the critical ray in the slower medium. The description is given via the parabolic equation method. The result involves a Pearcey-type integral. The approach is not based on the Fourier method and can be generalised to inhomogeneous media with curved interfaces. 
@article{ZNSL_2000_264_a8,
     author = {A. P. Kiselev and A. S. Starkov},
     title = {Parabolic equation and {Pearcey-type} integral for a transmitted wavefield},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {140--149},
     year = {2000},
     volume = {264},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_264_a8/}
}
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A. P. Kiselev; A. S. Starkov. Parabolic equation and Pearcey-type integral for a transmitted wavefield. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 29, Tome 264 (2000), pp. 140-149. http://geodesic.mathdoc.fr/item/ZNSL_2000_264_a8/