Geodesic
Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp
Matematičeskie zametki, Tome 108 (2020) no. 3, pp. 334-359

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We develop an approach to writing efficient short-wave asymptotics based on the representation of the Maslov canonical operator in a neighborhood of generic caustics in the form of special functions of a composite argument. A constructive method is proposed that allows expressing the canonical operator near a caustic cusp corresponding to the Lagrangian singularity of type $A_3$ (standard cusp) in terms of the Pearcey function and its first derivatives. It is shown that, conversely, the representation of a Pearcey type integral via the canonical operator turns out to be a very simple way to obtain its asymptotics for large real values of the arguments in terms of Airy functions and WKB-type functions.
Keywords: semiclassical asymptotics, canonical operator, caustic, Pearcey function
Mots-clés : cusp, efficient formula. 
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     author = {S. Yu. Dobrokhotov and V. E. Nazaikinskii},
     title = {Lagrangian {Manifolds} and {Efficient} {Short-Wave} {Asymptotics} in a {Neighborhood} of a {Caustic} {Cusp}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {334--359},
     publisher = {mathdoc},
     volume = {108},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_3_a1/}
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S. Yu. Dobrokhotov; V. E. Nazaikinskii. Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp. Matematičeskie zametki, Tome 108 (2020) no. 3, pp. 334-359. http://geodesic.mathdoc.fr/item/MZM_2020_108_3_a1/