New transformations for Painlevé’s third transcendent

DOI10.1090/S0002-9939-04-07087-XzbMath1045.34061arXivmath/0210019OpenAlexW1588193746MaRDI QIDQ4461149

Nicholas S. Witte

Publication date: 29 March 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210019

zbMATH Keywords

Bäcklund transformationsPainlevé equationstau-function

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Painlevé-type functions (33E17) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (8)

Parametrization of solutions of the Lewis metric by a Painlevé transcendent III ⋮ Isomonodromy for the degenerate fifth Painlevé equation ⋮ Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy ⋮ Series solution of Painlevé II in electrodiffusion: conjectured convergence ⋮ Emergent behaviour in electrodiffusion: Planck's other quanta ⋮ Folding transformations of the Painlevé equations ⋮ Solution of the equivalence problem for the third Painlevé equation ⋮ 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

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• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Mappings preserving locations of movable poles: II. The third and fifth Painlevé equations
• Solutions of the third Painlevé equation I
• Bäcklund Transformations and Solution Hierarchies for the Third Painlevé Equation
• On a unified approach to transformations and elementary solutions of Painlevé equations
• On One‐Parameter Families of Painlevé III
• Classical solutions of the third Painlevé equation
• Truncation-type methods and Bäcklund transformations for ordinary differential equations: the third and fifth Painlevé equations
• Rational Solutions of Painlevé Equations
• Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.
• Functional relations among solutions to the fifth Painlevé equation

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