On the identity of two \(q\)-discrete Painlevé equations and their geometrical derivation

DOI10.1155/ADE/2006/36397zbMath1140.39313OpenAlexW2072157145WikidataQ59212363 ScholiaQ59212363MaRDI QIDQ2472199

Tomoyuki Takenawa, Basile Grammaticos, Alfred Ramani

Publication date: 20 February 2008

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/54305

zbMATH Keywords

affine Weyl groupsgeometrical derivation\(q\)-discrete Painlevé equations

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) Difference equations, scaling ((q)-differences) (39A13)

Related Items (1)

An ultradiscrete matrix version of the fourth Painlevé equation

Cites Work

• Unnamed Item
• Self-duality and Schlesinger chains for the asymmetric \(\text{d-P}_{\text{II}}\) and \(\text{q-P}_{\text{III}}\) equations
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Discrete dynamical systems with \(W(A^{(1)}_{m-1} \times A^{(1)}_{n-1})\) symmetry
• Integrable mappings and soliton equations. II
• A \(q\)-analog of the sixth Painlevé equation
• On a novel \(q\)-discrete analogue of the Painlevé VI equation
• Generating discrete Painlevé equations from affine Weyl groups
• On the rational solutions of q-Painlevé V equation
• Do integrable mappings have the Painlevé property?
• Weyl Group Symmetry of Type D5(1) in the q-Painlevé V Equation

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