Construction of a Lax pair for the \(E_{6}^{(1)} \)q-Painlevé system

DOI10.3842/SIGMA.2012.097zbMath1383.33005arXiv1207.0041OpenAlexW2011946730MaRDI QIDQ352424

Nicholas S. Witte, Christopher Michael Ormerod

Publication date: 4 July 2013

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.0041

zbMATH Keywords

orthogonal polynomialsAskey tableisomonodromic deformationsdivided-difference operatorsnon-uniform latticessemi-classical weights

Mathematics Subject Classification ID

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) Painlevé-type functions (33E17) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items (7)

The Padé interpolation method applied to \(q\)-Painlevé equations. II (differential grid version) ⋮ Hypergeometric solutions for the \(q\)-Painlevé equation of type \({E^{(1)}_6}\) by the Padé method ⋮ A \(3 \times 3\) Lax form for the \(q\)-Painlevé equation of type \(E_6\) ⋮ Geometric aspects of Painlevé equations ⋮ The Padé interpolation method applied to \(q\)-Painlevé equations ⋮ Commutation relations and discrete garnier systems ⋮ The Padé interpolation method applied to additive difference Painlevé equations

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