dorsal/arxiv
View SchemaBilinear structure and Schlesinger transforms of the $q$-P$_{\rm III}$ and $q$-P$_{\rm VI}$ equations
| Authors | M. Jimbo, H. Sakai, A. Ramani, B. Grammaticos |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9601004 |
| URL | https://arxiv.org/abs/solv-int/9601004 |
| DOI | 10.1016/0375-9601(96)00336-2 |
Abstract
We show that the recently derived ($q$-) discrete form of the Painlev\'e VI equation can be related to the discrete P$_{\rm III}$, 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$_{\rm III}$ and $q$-P$_{\rm VI}$.
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"abstract": "We show that the recently derived ($q$-) discrete form of the Painlev\\\u0027e VI\nequation can be related to the discrete P$_{\\rm III}$, in particular if one\nuses the full freedom in the implementation of the singularity confinement\ncriterion. This observation is used here in order to derive the bilinear forms\nand the Schlesinger transformations of both $q$-P$_{\\rm III}$ and $q$-P$_{\\rm\nVI}$.",
"arxiv_id": "solv-int/9601004",
"authors": [
"M. Jimbo",
"H. Sakai",
"A. Ramani",
"B. Grammaticos"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/0375-9601(96)00336-2",
"title": "Bilinear structure and Schlesinger transforms of the $q$-P$_{\\rm III}$ and $q$-P$_{\\rm VI}$ equations",
"url": "https://arxiv.org/abs/solv-int/9601004"
},
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