Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp

S. Yu. Dobrokhotov ; V. E. Nazaikinskii

Matematičeskie zametki, Tome 108 (2020) no. 3, pp. 334-359.

Résumé

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.

Détail

Keywords: semiclassical asymptotics, canonical operator, caustic, Pearcey function
Mots-clés : cusp, efficient formula.

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