A \(\tau \)-function solution of the sixth Painlevé transcendent

DOI10.1007/s11232-009-0150-zzbMath1185.37137arXiv1011.1641OpenAlexW2010174645MaRDI QIDQ2269390

Yurii V. Brezhnev

Publication date: 16 March 2010

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

Full work available at URL: https://arxiv.org/abs/1011.1641

zbMATH Keywords

theta functionuniformizationelliptic functionPainlevé VI equationautomorphic function

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Painlevé-type functions (33E17)

Related Items (max. 100)

Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation. I. ⋮ On the convergence of formal exotic series solutions of an ODE ⋮ Pole distribution of PVI transcendents close to a critical point ⋮ On linear systems and \(\tau\) functions associated with Lamé's equation and Painlevé's equation VI ⋮ The sixth Painlevé transcendent and uniformization of algebraic curves ⋮ Form factor expansions in the 2D Ising model and Painlevé VI ⋮ A review of the sixth Painlevé equation

Cites Work

• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• Polynomial Hamiltonians associated with Painleve equations. II: Differential equations satisfied by polynomial Hamiltonians
• Self-dual \(SU(2)\)-invariant Einstein metrics and modular dependence of theta functions
• On a Schwarzian PDE associated with the KdV hierarchy
• The Painlevé III, V and VI transcendents as solutions of the Einstein-Weyl equations
• The Painlevé property. One century later
• Painlevé differential equations in the complex plane
• Self-dual Einstein metrics from the Painlevé VI equation
• 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
• The elliptic representation of the general Painlevé VI equation
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