Quadratic transformations for the sixth Painlevé equation

DOI10.1007/BF00401643zbMath0716.34075OpenAlexW1967460173MaRDI QIDQ752965

Alexander V. Kitaev

Publication date: 1991

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00401643

zbMATH Keywords

hypergeometric functionsPainlevé six equation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotic expansions of solutions to ordinary differential equations (34E05)

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Hamiltonians associated with the sixth Painlevé equation ⋮ Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation ⋮ Schlesinger transformations for Painlevé VI equation ⋮ Moyal Deformation of 2D Euler Equation and Discretization ⋮ Isomonodromic deformations and twisted Yangians arising in Teichmüller theory ⋮ Folding transformations of equations from the Gambier family ⋮ Flat structure on the space of isomonodromic deformations ⋮ Schlesinger transformations for algebraic Painlevé VI solutions ⋮ Cubic and Quartic Transformations of the Sixth Painlevé Equation in Terms of Riemann–Hilbert Correspondence ⋮ Folding transformations of the Painlevé equations ⋮ Ramified covers and tame isomonodromic solutions on curves ⋮ Algebraic solutions of the sixth Painlevé equation ⋮ Grothendieck’s dessins d’enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations ⋮ The fifty-two icosahedral solutions to Painlevé VI ⋮ Factorization of Ising correlations C(M, N) for ν = −k and M + N odd, M ⩽ N, T < T _c and their lambda extensions

Cites Work

• Monodromy problem and the boundary condition for some Painlevé equations
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• On a unified approach to transformations and elementary solutions of Painlevé equations

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