Bilinear structure and Schlesinger transforms of the $q$-P$_{\rm III}$ and $q$-P$_{\rm VI}$ equations

M. Jimbo; H. Sakai; A. Ramani; B. Grammaticos

doi:10.1016/0375-9601(96)00336-2

paper

Bilinear structure and Schlesinger transforms of the $q$ -P $_{III}$ and $q$ -P $_{VI}$ equations

arXiv:solv-int/9601004 · doi:10.1016/0375-9601(96)00336-2

Abstract

We show that the recently derived ( $q$ -) discrete form of the Painlevé VI equation can be related to the discrete P $_{III}$ , in particular if one uses the full freedom in the implementation of the singularity confinement criterion. This observation is used here in order to derive the bilinear forms and the Schlesinger transformations of both $q$ -P $_{III}$ and $q$ -P $_{VI}$ .

10 pages, Plain TeX

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Bilinear structure and Schlesinger transforms of the q-PIII​ and q-PVI​ equations

Abstract

Cited by in corpus (5)

Bilinear structure and Schlesinger transforms of the $q$ -P $_{III}$ and $q$ -P $_{VI}$ equations