Hypergeometric Solutions to an Ultradiscrete Painlevé Equation

DOI10.1142/S140292511000060XzbMath1191.39010arXivnlin/0610048OpenAlexW1745470200MaRDI QIDQ3565173

Christopher Michael Ormerod

Publication date: 2 June 2010

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

Full work available at URL: https://arxiv.org/abs/nlin/0610048

zbMATH Keywords

hypergeometric functionshypergeometric solutionstranscendental solutionsdiscrete Riccati type solutionsnon-Archimedean valuation over a fieldultradiscrete third Painlevé equation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (5)

Ultradiscrete analogue of the van der Pol equation ⋮ Bessel function type solutions of the ultradiscrete Painlevé III equation with parity variables ⋮ Ultradiscrete hard-spring equation and its phase plane analysis ⋮ Indeterminate solutions of the \(p\)-ultradiscrete equation and leading term analysis ⋮ Ultradiscrete analogues of the hard-spring equation and its conserved quantity

Cites Work

• Bilinear structure and Schlesinger transforms of the \(q\)-P\(_{III}\) and \(q\)-P\(_{VI}\) equations
• A \(q\)-analog of the sixth Painlevé equation
• The ultimate discretisation of the Painlevé equations
• Rational solutions for the discrete Painlevé II equation.
• Piecewise-linear soliton equations and piecewise-linear integrable maps
• Constructing solutions to the ultradiscrete Painlevé equations
• Discrete versions of the Painlevé equations
• Lax pairs for ultra-discrete Painlevé cellular automata
• Casorati determinant solutions for the discrete Painlevé III equation
• Ultradiscretization without positivity
• How to detect integrability in cellular automata
• The Linear q-Difference Equation of the Second Order

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