Self-duality and the Painleve transcendents

DOI10.1088/0951-7715/6/4/004zbMath0778.34004OpenAlexW2012868804MaRDI QIDQ3137376

N. M. J. Woodhouse, Lionel J. Mason

Publication date: 13 December 1993

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/6/4/004

zbMATH Keywords

self-dual Yang-Mills equationsPainlevé transcendental equationsdirect twistor transformthree-dimensional Abelian groups of conformal symmetries

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) 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) Yang-Mills and other gauge theories in quantum field theory (81T13) PDEs in connection with quantum mechanics (35Q40)

Related Items (13)

Singular instantons and Painlevé VI ⋮ The twistor theory of equations of KdV type. I ⋮ Equivariant connected sums of compact self-dual manifolds ⋮ Integrability, computation and applications ⋮ Integrable systems and reductions of the self-dual Yang–Mills equations ⋮ The fourth Painlevé equation and associated special polynomials ⋮ Self-dual Yang-Mills fields in \(d=4\) and integrable systems in \(1\leq d\leq 3\) ⋮ Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation ⋮ Necessary conditions for point equivalence of second-order ODEs to the sixth Painlevé equation ⋮ Bianchi Permutability for the Anti-Self-Dual Yang-Mills Equations ⋮ General Schlesinger Systems and Their Symmetry from the View Point of Twistor theory ⋮ Sheaf lines of Yang–Mills instanton sheaves ⋮ Null Kähler geometry and isomonodromic deformations

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