The Painlevé III, V and VI transcendents as solutions of the Einstein-Weyl equations

DOI10.1016/S0375-9601(00)00113-4zbMath0944.37042MaRDI QIDQ1569584

Wolfgang K. Schief

Publication date: 3 July 2000

Published in: Physics Letters. A (Search for Journal in Brave)

zbMATH Keywords

symmetry reductionPainlevé V equationsintegable Loewner-Konopelchenko-Rogers systemintegrable Ernst-Weyl equationPainlevé III equationsPainlevé VI equations

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Painlevé-type functions (33E17)

Related Items (6)

On Laplace–Darboux-type sequences of generalized Weingarten surfaces ⋮ Painlevé VI and the Unitary Jacobi Ensembles ⋮ Integrability aspects of a Schwarzian PDE ⋮ A family of integrable nonlinear equations of hyperbolic type ⋮ A \(\tau \)-function solution of the sixth Painlevé transcendent ⋮ On the geometry of the Painlevé V equation and a Bäcklund transformation

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