Study of $q$-Garnier system by Padé method

Abstract

We give a simple form of the evolution equation and a scalar Lax pair for the $q$-Garnier system. Some reductions to the $q$-Painlevé equations and the autonomous case as a generalized QRT system are discussed. Using two kinds of Padé problems on differential grid and $q$-grid, we derive some special solutions of the $q$-Garnier system in terms of the $q$-Appell Lauricella function and the generalized $q$-hypergeometric function.

21 pages

References in corpus (2)

• A Lax Formalism for the Elliptic Difference Painlevé Equation
• Lax pairs for additive difference Painlevé equations

Cited by in corpus (6)

• Variations of $q$-Garnier system
• An Elliptic Garnier System from Interpolation
• Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
• A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$
• Lax pairs for additive difference Painlevé equations
• On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions