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

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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 150, Number 1, Pages 143–151
DOI: https://doi.org/10.4213/tmf5970 (Mi tmf5970)

This article is cited in 11 scientific papers (total in 11 papers)

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

S. Yu. Slavyanov^a, F. R. Vukailovich^b

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

Full-text PDF (382 kB) Citations (11)

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

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.

Received: 29.08.2006

English version:
Theoretical and Mathematical Physics, 2007, Volume 150, Issue 1, Pages 123–131
DOI: https://doi.org/10.1007/s11232-007-0009-0

Bibliographic databases:

Language: Russian

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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https://doi.org/10.4213/tmf5970

https://www.mathnet.ru/eng/tmf/v150/i1/p143

This publication is cited in the following 11 articles:

Slavyanov S., Stesik O., “Antiquantization as a Specific Way From the Statistical Physics to the Regular Physics”, Physica A, 521 (2019), 512–518
A. A. Salatich, S. Yu. Slavyanov, O. L. Stesik, “Sistemy ODU pervogo poryadka, porozhdayuschie konflyuentnye uravneniya Goina”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye metody. XXXI, Zap. nauchn. sem. POMI, 485, POMI, SPb., 2019, 187–194
J. Math. Sci. (N. Y.), 209:6 (2015), 910–921
S. Yu. Slavyanov, “Antiquantization and the corresponding symmetries”, Theoret. and Math. Phys., 185:1 (2015), 1522–1526
Slavyanov S.Y., “Relations Between Linear Equations and Painlevé'S Equations”, Constr. Approx., 39:1, SI (2014), 75–83
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
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
S.Yu. Slavyanov, A.Ya. Kazakov, F. R. Vukajlović, “RELATIONS BETWEEN HEUN EQUATIONS AND PAINLEVE EQUATIONS”, Albanian J. Math., 4:4 (2010)
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
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
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

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

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