S. Yu. Slavyanov, “Isomonodromic deformations of Heun and Painlevé equations”, TMF, 123:3 (2000), 395–406; Theoret. and Math. Phys., 123:3 (2000), 744

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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 123, Number 3, Pages 395–406
DOI: https://doi.org/10.4213/tmf611 (Mi tmf611)

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

Isomonodromic deformations of Heun and Painlevé equations

S. Yu. Slavyanov

Saint-Petersburg State University

Full-text PDF (230 kB) Citations (17)

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DOI: https://doi.org/10.4213/tmf611

Abstract: Continuing the study of the relationship between the Heun and the Painlevé classes of equations reported in two previous papers, we formulate and prove the main theorem expressing this relationship. We give a Hamiltonian interpretation of the isomonodromic deformation condition and propose an alternative classification of the Painlevé equations, which includes ten equations.

Received: 07.10.1999

English version:
Theoretical and Mathematical Physics, 2000, Volume 123, Issue 3, Pages 744–753
DOI: https://doi.org/10.1007/BF02551029

Bibliographic databases:

Language: Russian

Citation: S. Yu. Slavyanov, “Isomonodromic deformations of Heun and Painlevé equations”, TMF, 123:3 (2000), 395–406; Theoret. and Math. Phys., 123:3 (2000), 744–753

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf611

https://doi.org/10.4213/tmf611

https://www.mathnet.ru/eng/tmf/v123/i3/p395

This publication is cited in the following 17 articles:

S. I. Tertichniy, “On the Monodromy-Preserving Deformation of a Double Confluent Heun Equation”, Proc. Steklov Inst. Math., 326 (2024), 303–338
Xia J., Xu Sh.-X., Zhao Yu.-Q., “Isomonodromy Sets of Accessory Parameters For Heun Class Equations”, Stud. Appl. Math., 146:4 (2021), 901–952
S. I. Tertychnyi, “Solution space monodromy of a special double confluent Heun equation and its applications”, Theoret. and Math. Phys., 201:1 (2019), 1426–1441
Combot T., “Integrability of the One Dimensional Schrodinger Equation”, J. Math. Phys., 59:2 (2018), 022105
S. Yu. Slavyanov, O. L. Stesik, “Antiquantization of deformed Heun-class equations”, Theoret. and Math. Phys., 186:1 (2016), 118–125
Slavyanov S., “Antiquantization of Deformed Equations of Heun Class”, Proceedings of the International Conference Days on Diffraction 2015, IEEE, 2015, 310–312
Rumanov I., “Beta Ensembles, Quantum Painlevé Equations and Isomonodromy Systems”, Algebraic and Analytic Aspects of Integrable Systems and Painlev? Equations, Contemporary Mathematics, 651, ed. Dzhamay A. Maruno K. Ormerod C., Amer Mathematical Soc, 2015, 125–155
S. Slavyanov, 2015 Days on Diffraction (DD), 2015, 1
A. Zabrodin, A. Zotov, “Classical-quantum correspondence and functional relations for Painlevé equations”, Constr. Approx., 41:3 (2015), 385–423
V. V. Tsegel'nik, “Hamiltonians associated with the third and fifth Painlevé equations”, Theoret. and Math. Phys., 162:1 (2010), 57–62
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
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
S. Yu. Slavyanov, F. R. Vukailovich, “Isomonodromic deformations and “antiquantization” for the simplest ordinary differential equations”, Theoret. and Math. Phys., 150:1 (2007), 123–131
V. V. Tsegel'nik, “Hamiltonians associated with the sixth Painlevé equation”, Theoret. and Math. Phys., 151:1 (2007), 482–491
Tarasov, VF, “The Heun-Schrodinger radial equation with two auxiliary parameters for H-like atoms”, Modern Physics Letters B, 16:25 (2002), 937
Slavyanov S.Y., “Kovalevskaya's dynamics and Schrodinger equations of Heun class”, Operator Methods in Ordinary and Partial Differential Equations, Operator Theory : Advances and Applications, 132, 2002, 395–402

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

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Abstract page:	616
Full-text PDF :	300
References:	67
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