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New representations of the Maslov canonical operator and localized asymptotic solutions for strictly hyperbolic systems

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Abstract

A procedure for constructing asymptotic solutions of strictly hyperbolic systems of partial differential equations is described in general terms. On the basis of the obtained results, an asymptotic solution of a three-dimensional wave equation with variable velocity is constructed. The case of a cylindrically symmetric velocity is considered.

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Authors and Affiliations

  1. Institute for Problems of Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, korp. 1, Moscow, 119526, Russia

    A. I. Allilueva

  2. Moscow Institute of Physics and Technology, State University, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    A. I. Allilueva, S. Yu. Dobrokhotov & S. A. Sergeev

  3. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    A. I. Shafarevich

Authors
  1. A. I. Allilueva
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  2. S. Yu. Dobrokhotov
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  3. S. A. Sergeev
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  4. A. I. Shafarevich
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Correspondence to A. I. Allilueva.

Additional information

Original Russian Text © A.I. Allilueva, S.Yu. Dobrokhotov, S.A. Sergeev, A.I. Shafarevich, 2015, published in Doklady Akademii Nauk, 2015, Vol. 464, No. 3, pp. 261–266.

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Allilueva, A.I., Dobrokhotov, S.Y., Sergeev, S.A. et al. New representations of the Maslov canonical operator and localized asymptotic solutions for strictly hyperbolic systems. Dokl. Math. 92, 548–553 (2015). https://doi.org/10.1134/S1064562415050129

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  • DOI: https://doi.org/10.1134/S1064562415050129

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