Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation

DOI10.1007/s11232-006-0040-6zbMath1177.34114OpenAlexW2004792267MaRDI QIDQ1047989

D. P. Novikov

Publication date: 9 January 2010

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-006-0040-6

zbMATH Keywords

Heun equationPainlevé VI equationEuler integral transformationokamoto transformationschlesinger transformation

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (6)

The \(2\times 2\) matrix Schlesinger system and the Belavin-Polyakov-Zamolodchikov system ⋮ Isomonodromic deformations and ``antiquantization for the simplest ordinary differential equations ⋮ Notes on Umemura polynomials ⋮ On the linearization of the Painlevé III–VI equations and reductions of the three-wave resonant system ⋮ Series solutions of the non-stationary Heun equation ⋮ Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions

Cites Work

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• Monodromy problem and the boundary condition for some Painlevé equations
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• Polynomial Hamiltonians associated with Painleve equations. I
• Integral relations for Heun-class special functions
• Integral symmetries, integral invariants, and monodromy matrices for ordinary differential equations
• Canonical structure and symmetries of the Schlesinger equations
• IRREGULAR ISOMONODROMIC DEFORMATIONS FOR GARNIER SYSTEMS AND OKAMOTO'S CANONICAL TRANSFORMATIONS
• From Klein to Painlevé via Fourier, Laplace and Jimbo
• Bäcklund Transformations of the Sixth Painlevé Equation in Terms of Riemann-Hilbert Correspondence

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