Bilinear structure and Schlesinger transforms of the \(q\)-P\(_{III}\) and \(q\)-P\(_{VI}\) equations

DOI10.1016/0375-9601(96)00336-2zbMath0911.34007arXivsolv-int/9601004OpenAlexW1612588391MaRDI QIDQ1914571

Alfred Ramani, Michio Jimbo, Basile Grammaticos, Hidetaka Sakai

Publication date: 18 June 1996

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

Full work available at URL: https://arxiv.org/abs/solv-int/9601004

zbMATH Keywords

bilinear formsSchlesinger transformations

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25)

Related Items (14)

QRT maps and related Laurent systems ⋮ Reductions of a two-dimensional sine-Gordon system to the sixth Painlevé equation ⋮ The ultimate discretisation of the Painlevé equations ⋮ A bilinear approach to discrete Miura transformations. ⋮ Bilinear, trilinear forms, and exact solution of certain fourth order integrable difference equations ⋮ Hypergeometric Solutions to an Ultradiscrete Painlevé Equation ⋮ On the discrete form of the Fokas--Ablowitz equation ⋮ Integrability in a discrete world ⋮ Hierarchies of exact solutions for the discrete third Painlevé equation ⋮ From discrete to continuous Painlevé equations: a bilinear approach ⋮ A Unified Description of the Asymmetric q-PV and d-PIV Equations and their Schlesinger Transformations ⋮ Constructing discrete Painlevé equations: from E8(1) to A1(1) and back ⋮ Proceedings of the 12th international workshop on nonlinear evolution equations and dynamical systems (NEEDS '98), Leeds, UK, June 21--28, 1998. Transl. from the Russian ⋮ A simplified version of higher covariant derivative regularization

Cites Work

• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Bilinear discrete Painleve equations
• Miura transforms for discrete Painleve equations
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?

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