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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 2, Pages 53–96 (Mi izv8470)  

This article is cited in 17 scientific papers (total in 17 papers)

New integral representations of the Maslov canonical operator in singular charts

S. Yu. Dobrokhotovab, V. E. Nazaikinskiiab*, A. I. Shafarevichabcd

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
c Lomonosov Moscow State University
d National Research Centre "Kurchatov Institute", Moscow

Abstract: We construct a new integral representation of the Maslov canonical operator convenient in numerical-analytical calculations, present an algorithm implementing this representation, and consider a number of examples.

Keywords: Maslov canonical operator, Fourier integral operator, integral representation, asymptotic formula.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00521-
Ministry of Education and Science of the Russian Federation -581.2014.1
The research was supported by the Russian Foundation for Basic Research under grants nos. 14-01-00521-a and 13-01-00664-a and by the programme ‘Leading Scientific Schools’ under grant no. NSh-581.2014.1).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/im8470

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English version:
Izvestiya: Mathematics, 2017, 81:2, 286–328

Bibliographic databases:

UDC: 517.9
MSC: Primary 81Q20; Secondary 53D12, 35C20
Received: 12.11.2015
Revised: 15.03.2016

Citation: S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “New integral representations of the Maslov canonical operator in singular charts”, Izv. RAN. Ser. Mat., 81:2 (2017), 53–96; Izv. Math., 81:2 (2017), 286–328

Citation in format AMSBIB
\by S.~Yu.~Dobrokhotov, V.~E.~Nazaikinskii, A.~I.~Shafarevich
\paper New integral representations of the Maslov canonical operator in singular charts
\jour Izv. RAN. Ser. Mat.
\yr 2017
\vol 81
\issue 2
\pages 53--96
\jour Izv. Math.
\yr 2017
\vol 81
\issue 2
\pages 286--328

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    This publication is cited in the following articles:
    1. S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. A. Tolchennikov, “Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge”, Russ. J. Math. Phys., 24:4 (2017), 544–552  crossref  mathscinet  zmath  isi  scopus
    2. A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, M. Rouleux, “The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides”, Dokl. Math., 96:1 (2017), 406–410  crossref  mathscinet  zmath  isi  scopus
    3. S. Yu. Dobrokhotov, S. Ya. Sekerzh-Zen'kovich, A. A. Tolchennikov, “Exact and asymptotic solutions of the Cauchy-Poisson problem with localized initial conditions and a constant function of the bottom”, Russ. J. Math. Phys., 24:3 (2017), 310–321  crossref  mathscinet  zmath  isi  scopus
    4. S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Waves on the free surface described by linearized equations of hydrodynamics with localized right-hand sides”, Russ. J. Math. Phys., 25:1 (2018), 1–16  crossref  mathscinet  zmath  isi  scopus
    5. A. Anikin, S. Dobrokhotov, V. Nazaikinskii, M. Rouleux, “Semi-classical Green functions”, 2018 Days on Diffraction (DD), International Conference on Days on Diffraction (DD) (St Petersburg, RUSSIA, JUN 04–08, 2018), eds. O. Motygin, A. Kiselev, L. Goray, A. Kazakov, A. Kirpichnikova, M. Perel, IEEE, 2018, 17–23  isi
    6. S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Asymptotic localized solutions of the shallow water equations over a nonuniform bottom”, Proceedings of the 44Th International Conference “Applications of Mathematics in Engineering and Economics”, AIP Conf. Proc., 2048, Amer. Inst. Phys., 2018, 040026  crossref  isi  scopus
    7. Reijnders K.J.A., Minenkov D.S., Katsnelson I M., Dobrokhotov S.Yu., “Electronic Optics in Graphene in the Semiclassical Approximation”, Ann. Phys., 397 (2018), 65–135  crossref  mathscinet  zmath  isi  scopus
    8. S. Yu. Dobrokhotov, A. A. Tolchennikov, “Solution of the two-dimensional Dirac equation with a linear potential and a localized initial condition”, Russ. J. Math. Phys., 26:2 (2019), 139–151  crossref  mathscinet  zmath  isi  scopus
    9. S. A. Sergeev, “Asymptotic Solutions of the Cauchy Problem with Localized Initial Data for a Finite-Difference Scheme Corresponding to the One-Dimensional Wave Equation”, Math. Notes, 106:5 (2019), 800–813  mathnet  crossref  crossref  mathscinet  isi  elib
    10. P. S. Petrov, S. A. Sergeev, A. A. Tolchennikov, “On the application of asymptotic formulae based on the modified maslov canonical operator to the modeling of acoustic pulses propagation in three-dimensional shallow-water waveguides”, Acoust. Phys., 65:6 (2019), 716–723  crossref  mathscinet  isi
    11. V. V. Grushin, S. A. Sergeev, “Asymptotics of the propagation problem for linear waves on a two-dimensional lattice and modified Maslov's canonical operator”, Russ. J. Math. Phys., 27:1 (2020), 31–47  crossref  mathscinet  zmath  isi  scopus
    12. S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Uniformization of Equations with Bessel-Type Boundary Degeneration and Semiclassical Asymptotics”, Math. Notes, 107:5 (2020), 847–853  mathnet  crossref  crossref  mathscinet  isi  elib
    13. S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp”, Math. Notes, 108:3 (2020), 318–338  mathnet  crossref  crossref  mathscinet  isi  elib
    14. S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. A. Tolchennikov, “Uniform formulas for the asymptotic solution of a linear pseudodifferential equation describing water waves generated by a localized source”, Russ. J. Math. Phys., 27:2 (2020), 185–191  crossref  mathscinet  zmath  isi
    15. S. A. Sergeev, “Asymptotics of the Head Wave in the Cauchy Problem for a Difference Scheme Corresponding to the Two-Dimensional Wave Equation with Localized Initial Data”, Math. Notes, 109:6 (2021), 918–931  mathnet  crossref  crossref  isi  elib
    16. S. Yu. Dobrokhotov, D. S. Minenkov, V. E. Nazaikinskii, “Representations of Bessel functions via the Maslov canonical operator”, Theoret. and Math. Phys., 208:2 (2021), 1018–1037  mathnet  crossref  crossref  isi  elib
    17. S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Effektivnye asimptotiki reshenii zadachi Koshi s lokalizovannymi nachalnymi dannymi dlya lineinykh sistem differentsialnykh i psevdodifferentsialnykh uravnenii”, UMN, 76:5(461) (2021), 3–80  mathnet  crossref
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