Geodesic
New formulas for Maslov's canonical operator in a~neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 3, pp. 355-386

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We suggest a new representation of Maslov's canonical operator in a neighborhood of caustics using a special class of coordinate systems (eikonal coordinates) on Lagrangian manifolds. We present the results in the two-dimensional case and illustrate them with examples.
Keywords: semiclassical asymptotics, focal point, caustic, integral representation, Bessel function, Schrödinger equation, wave beam. 
@article{TMF_2013_177_3_a0,
     author = {S. Yu. Dobrokhotov and G. N. Makrakis and V. E. Nazaikinskii and T. Ya. Tudorovskii},
     title = {New formulas for {Maslov's} canonical operator in a~neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--386},
     publisher = {mathdoc},
     volume = {177},
     number = {3},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_177_3_a0/}
}
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S. Yu. Dobrokhotov; G. N. Makrakis; V. E. Nazaikinskii; T. Ya. Tudorovskii. New formulas for Maslov's canonical operator in a~neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 3, pp. 355-386. http://geodesic.mathdoc.fr/item/TMF_2013_177_3_a0/