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TMF, 2007, Volume 150, Number 1, Pages 143–151 (Mi tmf5970)  

This article is cited in 9 scientific papers (total in 9 papers)

Isomonodromic deformations and "antiquantization" for the simplest ordinary differential equations

S. Yu. Slavyanova, F. R. Vukailovichb

a Saint-Petersburg State University
b Vinca Institute of Nuclear Sciences

Abstract: We consider three different models of linear differential equations and their isomonodromic deformations. We show that each of the models has its own specificity, although all of them lead to the same final result. It turns out that isomonodromic deformations are closely related to the Hamiltonian structure of both classical mechanics and quantum mechanics.

Keywords: isomonodromic deformations, antiquantization, accessory parameter, inessential singularity

DOI: https://doi.org/10.4213/tmf5970

Full text: PDF file (382 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 150:1, 123–131

Bibliographic databases:

Received: 29.08.2006

Citation: S. Yu. Slavyanov, F. R. Vukailovich, “Isomonodromic deformations and "antiquantization" for the simplest ordinary differential equations”, TMF, 150:1 (2007), 143–151; Theoret. and Math. Phys., 150:1 (2007), 123–131

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v150/i1/p143

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation”, Theoret. and Math. Phys., 155:2 (2008), 722–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. B. I. Suleimanov, ““Quantizations” of the second Painlevé equation and the problem of the equivalence of its $L$$A$ pairs”, Theoret. and Math. Phys., 156:3 (2008), 1280–1291  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. M. V. Babich, “On canonical parametrization of the phase spaces of equations of isomonodromic deformations of Fuchsian systems of dimension $2\times 2$. Derivation of the Painlevé VI equation”, Russian Math. Surveys, 64:1 (2009), 45–127  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. Mylläri, S. Yu. Slavyanov, “Integrable dynamical systems generated by quantum models with an adiabatic parameter”, Theoret. and Math. Phys., 166:2 (2011), 224–227  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    5. Slavyanov S.Yu., “Derivation of Painlevé equations by antiquantization”, Painleve Equations and Related Topics (2012), Degruyter Proceedings in Mathematics, eds. Bruno A., Batkhin A., Walter de Gruyter & Co, 2012, 253–256  mathscinet  isi
    6. Slavyanov S.Y., “Relations Between Linear Equations and Painlevé'S Equations”, Constr. Approx., 39:1, SI (2014), 75–83  crossref  mathscinet  zmath  isi  scopus
    7. J. Math. Sci. (N. Y.), 209:6 (2015), 910–921  mathnet  crossref
    8. S. Yu. Slavyanov, “Antiquantization and the corresponding symmetries”, Theoret. and Math. Phys., 185:1 (2015), 1522–1526  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. Slavyanov S., Stesik O., “Antiquantization as a Specific Way From the Statistical Physics to the Regular Physics”, Physica A, 521 (2019), 512–518  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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