A q-anaolg of the sixth Painlevé equation

1995/07/31 by Michio Jimbo, Hidetaka Sakai · 8 citations
Computer Science · Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Polynomial and algebraic computation #chao-dyn #nlin.CD #nlin.SI #solv-int

paper · pdf · doi:10.1007/bf00398316

8 pages, LaTeX file (Two misprints corrected)

arxiv created 1995/08/15 · openalex publication_date 1996/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A q-difference analog of the sixth Painlevé equation is presented. It arises as the condition for preserving the connection matrix of linear q-difference equations, in close analogy with the monodromy preserving deformation of linear differential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed.

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• Quantizing the Discrete Painlevé VI Equation: The Lax Formalism
• A Tau function for q-Painlevé VI as a Fredholm determinant
• Degenerations of Ruijsenaars-van Diejen operator and q-Painleve equations
• A geometric approach to singularity confinement and algebraic entropy