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”, TMF, 2013, Volume 177, Number 3,Pages <nobr>355–386</nobr>

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TMF, 2013 Volume 177, Number 3, Pages 355–386 (Mi tmf8462)

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New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics

S. Yu. Dobrokhotov^ab, G. N. Makrakis^cd, V. E. Nazaikinskii^ab, T. Ya. Tudorovskii^e

^a Ishlinsky Institute for Problems in Mechanics, Moscow, Russia
^b Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
^c Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece
^d Department of Mathematics and Applied Mathematics, University of Crete, Crete, Greece
^e Radboud University Nijmegen, Institute for Molecules and Materials, Nijmegen, The Netherlands

Abstract: 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.

Received: 24.12.2012
Revised: 24.07.2013

DOI: 10.4213/tmf8462

English version: Theoretical and Mathematical Physics, 2013, 177:3, 1579–1605

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