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A $q$-anaolg of the sixth Painlev\'e equation

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arxiv chao-dyn/9507010 v2 pith:2ZKHHHFE submitted 1995-07-31 chao-dyn nlin.CDnlin.SIsolv-int

Michio Jimbo , Hidetaka Sakai (Department of Mathematics , Kyoto Univ.) This is my paper · ORCID
classification chao-dynnlin.CDnlin.SIsolv-int
keywords differenceequationequationslinearpainlevpreservingsixthanalog
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abstract

A $q$-difference analog of the sixth Painlev\'e 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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  1. Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models

    hep-th 2019-08 conditional novelty 5.0 of 10

    The q-deformed conformal matrix model partition function, after a Fourier transform, is a Toda tau-function whose shifted ratios satisfy the discrete Painleve q-PVI equation, with the string equation supplied by Viras...

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