A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation”, TMF, 155:2 (2008), 252–264; Theoret. and Math. Phys., 155:2 (2008), 722

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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 155, Number 2, Pages 252–264
DOI: https://doi.org/10.4213/tmf6209 (Mi tmf6209)

This article is cited in 23 scientific papers (total in 23 papers)

Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation

A. Ya. Kazakov^a, S. Yu. Slavyanov^b

^a Saint-Petersburg State University of Aerospace Instrumentation
^b Saint-Petersburg State University

Full-text PDF (462 kB) Citations (23)

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DOI: https://doi.org/10.4213/tmf6209

Abstract: Euler integral transformations relate solutions of ordinary linear differential equations and generate integral representations of the solutions in a number of cases or relations between solutions of constrained equations (Euler symmetries) in some other cases. These relations lead to the corresponding symmetries of the monodromy matrices. We discuss Euler symmetries in the case of the simplest Fuchsian system that is equivalent to a deformed Heun equation, which is in turn related to the Painlevé PVI equation. The existence of integral symmetries of the deformed Heun equation leads to the corresponding symmetries of the PVI equation.

Keywords: Euler transformation, Heun equation, Painlevé equation.

Received: 29.10.2007

English version:
Theoretical and Mathematical Physics, 2008, Volume 155, Issue 2, Pages 722–733
DOI: https://doi.org/10.1007/s11232-008-0062-3

Bibliographic databases:

Language: Russian

Citation: A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation”, TMF, 155:2 (2008), 252–264; Theoret. and Math. Phys., 155:2 (2008), 722–733

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Linking options:

https://www.mathnet.ru/eng/tmf6209

https://doi.org/10.4213/tmf6209

https://www.mathnet.ru/eng/tmf/v155/i2/p252

This publication is cited in the following 23 articles:

Kouichi Takemura, 2021 Days on Diffraction (DD), 2021, 152
A. Ya. Kazakov, “Integralnaya simmetriya Eilera i asimptotika monodromii dlya uravnenii Goina”, Matematicheskie voprosy teorii rasprostraneniya voln. 50, Posvyaschaetsya devyanostoletiyu Vasiliya Mikhailovicha BABIChA, Zap. nauchn. sem. POMI, 493, POMI, SPb., 2020, 186–199
Babich M., Slavyanov S., “Antiquantization, Isomonodromy, and Integrability”, J. Math. Phys., 59:9, SI (2018), 091416
M. V. Babich, S. Yu. Slavyanov, “Links from second-order Fuchsian equations to first-order linear systems”, J. Math. Sci. (N. Y.), 240:5 (2019), 646–650
S. Yu. Slavyanov, “Symmetries and apparent singularities for the simplest Fuchsian equations”, Theoret. and Math. Phys., 193:3 (2017), 1754–1760
Takemura K., “Integral Transformation of Heun'S Equation and Some Applications”, J. Math. Soc. Jpn., 69:2 (2017), 849–891
S. Yu. Slavyanov, D. F. Shat'ko, A. M. Ishkhanyan, T. A. Rotinyan, “Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients”, Theoret. and Math. Phys., 189:3 (2016), 1726–1733
S. Yu. Slavyanov, O. L. Stesik, “Symbolic generation of Painlevé equations”, J. Math. Sci. (N. Y.), 224:2 (2017), 345–348
Ishkhanyan A.M., “A singular Lambert- W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions”, Mod. Phys. Lett. A, 31:33 (2016), 1650177
Chen Zh., Kuo T.-J., Lin Ch.-Sh., “Hamiltonian system for the elliptic form of Painlevé VI equation”, J. Math. Pures Appl., 106:3 (2016), 546–581
S. Yu. Slavyanov, “Polynomial degree reduction of a Fuchsian $2{\times}2$ system”, Theoret. and Math. Phys., 182:2 (2015), 182–188
Leroy C., Ishkhanyan A.M., “Expansions of the Solutions of the Confluent Heun Equation in Terms of the Incomplete Beta and the Appell Generalized Hypergeometric Functions”, Integral Transform. Spec. Funct., 26:6 (2015), 451–459
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
Shahverdyan T.A., Ishkhanyan T.A., Grigoryan A.E., Ishkhanyan A.M., “Analytic Solutions of the Quantum Two-State Problem in Terms of the Double, Bi- and Triconfluent Heun Functions”, J. Contemp. Phys.-Armen. Acad. Sci., 50:3 (2015), 211–226
Slavyanov S.Y., “Relations Between Linear Equations and Painlevé'S Equations”, Constr. Approx., 39:1, SI (2014), 75–83
A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for the confluent Heun equation and symmetries of the Painlevé equation PV”, Theoret. and Math. Phys., 179:2 (2014), 543–549
A. Ya. Kazakov, “Integral symmetry for the confluent Heun equation with added apparent singularity”, J. Math. Sci. (N. Y.), 214:3 (2016), 268–276
Kazakov A.Ya., Slavyanov S.Yu., “Integral Symmetries for Confluent Heun Equations and Symmetries of Painlevé Equation P-5”, Painleve Equations and Related Topics (2012), Degruyter Proceedings in Mathematics, eds. Bruno A., Batkhin A., Walter de Gruyter & Co, 2012, 237–239
S.Yu. Slavyanov, A.Ya. Kazakov, F. R. Vukajlović, “RELATIONS BETWEEN HEUN EQUATIONS AND PAINLEVE EQUATIONS”, Albanian J. Math., 4:4 (2010)

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

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