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TMF, 2000, Volume 123, Number 3, Pages 395–406 (Mi tmf611)  

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

Isomonodromic deformations of Heun and Painlevé equations

S. Yu. Slavyanov

Saint-Petersburg State University

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.

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

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English version:
Theoretical and Mathematical Physics, 2000, 123:3, 744–753

Bibliographic databases:

Received: 07.10.1999

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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\jour Theoret. and Math. Phys.
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\pages 744--753
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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. Tarasov, VF, “The Heun-Schrodinger radial equation with two auxiliary parameters for H-like atoms”, Modern Physics Letters B, 16:25 (2002), 937  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. 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  mathscinet  zmath  isi
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. V. Tsegel'nik, “Hamiltonians associated with the sixth Painlevé equation”, Theoret. and Math. Phys., 151:1 (2007), 482–491  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. 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
    6. 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
    7. V. V. Tsegel'nik, “Hamiltonians associated with the third and fifth Painlevé equations”, Theoret. and Math. Phys., 162:1 (2010), 57–62  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Slavyanov S., “Antiquantization of Deformed Equations of Heun Class”, Proceedings of the International Conference Days on Diffraction 2015, IEEE, 2015, 310–312  isi
    9. 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  crossref  mathscinet  zmath  isi
    10. S. Yu. Slavyanov, O. L. Stesik, “Antiquantization of deformed Heun-class equations”, Theoret. and Math. Phys., 186:1 (2016), 118–125  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. Combot T., “Integrability of the One Dimensional Schrodinger Equation”, J. Math. Phys., 59:2 (2018), 022105  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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