A Unified Description of the Asymmetric q-PV and d-PIV Equations and their Schlesinger Transformations

DOI10.2991/jnmp.2003.10.2.5zbMath1034.34104arXivnlin/0310050OpenAlexW3104059196MaRDI QIDQ4707380

Alfred Ramani, Yasuhiro Ohta, Basile Grammaticos

Publication date: 13 October 2003

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0310050

zbMATH Keywords

affine Weyl groupSchlesinger transformationsdiscrete analogues of the Painlevé VI equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (8)

Moduli spaces of \(d\)-connections and difference Painlevé equations ⋮ On some applications of Sakai's geometric theory of discrete Painlevé equations ⋮ Hypergeometric solutions for the \(q\)-Painlevé equation of type \({E^{(1)}_6}\) by the Padé method ⋮ Strongly asymmetric discrete Painlevé equations: The additive case ⋮ On the discrete form of the Fokas--Ablowitz equation ⋮ Strongly asymmetric discrete Painlevé equations: The multiplicative case ⋮ τ-function of discrete isomonodromy transformations and probability ⋮ Bäcklund transformations for discrete Painlevé equations: discrete P\(_{\text{II}}\)-P\(_{\text{V}}\)

Cites Work

• Self-duality and Schlesinger chains for the asymmetric \(\text{d-P}_{\text{II}}\) and \(\text{q-P}_{\text{III}}\) equations
• Schlesinger transforms for the discrete Painlevé IV equation
• Bilinear structure and Schlesinger transforms of the \(q\)-P\(_{III}\) and \(q\)-P\(_{VI}\) equations
• A \(q\)-analog of the sixth Painlevé equation
• A differential equation for orthogonal polynomials
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?
• A study of the alternate discrete Painlevé II equation

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