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Mat. Zametki, 2024 Volume 116, Issue 3, Pages 388–395 (Mi mzm14415)

Uniform formulas for the asymptotic solution near the leading front for Maxwell's equations with temporal dispersion and localized initial data

S. Yu. Dobrokhotov, A. A. Tolchennikov

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow

Abstract: Maxwell's equations with temporal dispersion and localized initial data are considered. Using the Maslov canonical operator, we construct a uniform asymptotic solution expressed in terms of the derivative of the Airy function of complicated argument, in the neighborhood of the regular points of the leading wave front.

Keywords: Maxwell's equations, localized initial data, Maslov canonical operator.

UDC: 517.928

Received: 05.12.2023
Revised: 10.04.2024

DOI: 10.4213/mzm14415


 English version:
Mathematical Notes, 2024, 116:3, 458–464


© Steklov Math. Inst. of RAS, 2024