A 𝑞-analogue of the Drinfeld-Sokolov Hierarchy of Type 𝐴 and 𝑞-Painlevé System

DOI10.1090/conm/651/13037zbMath1346.39010arXiv1105.4240OpenAlexW4255849961MaRDI QIDQ2990220

Takao Suzuki

Publication date: 29 July 2016

Published in: Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.4240

zbMATH Keywords

affine Weyl groupsintegral representationPainlevé equations\(q\)-hypergeometric functionDrinfeld-Sokolov hierarchysystem of \(q\)-difference equations

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) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Discrete version of topics in analysis (39A12) Difference equations, scaling ((q)-differences) (39A13) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

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The Padé interpolation method applied to \(q\)-Painlevé equations. II (differential grid version) ⋮ A \(3 \times 3\) Lax form for the \(q\)-Painlevé equation of type \(E_6\) ⋮ A variation of the \(q\)-Painlevé system with affine Weyl group symmetry of type \(E_7^{(1)}\) ⋮ Unnamed Item ⋮ Variations of theq-Garnier system ⋮ A Lax formulation of a generalized \(q\)-Garnier system ⋮ Study of <i>q</i>-Garnier System by Padé Method ⋮ An affine Weyl group action on the basic hypergeometric series arising from the \(q\)-Garnier system ⋮ A q-analogue of the matrix sixth Painlevé system

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