Rational solutions of difference Painlevé equations
type: Item
instance of: scholarly article
title: Rational solutions of difference Painlevé equations
zbMATH Open document ID: 1259.39014
author: Shun Shimomura
published in: Tokyo Journal of Mathematics
publication date: 2012-08-29T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tjm/1342701346
review text: The author captures all rational solutions of some difference Painlevé equations of PI and PII types. For non-autonomous cases it is shown that all rational solutions of the difference PII equations are generated by successive applications of auto-Bäcklund transformations to the seed solution vanishing identically, and that other equations of PI type admit no rational solutions. For autonomous cases all nontrivial rational solutions are obtained, and they exist under a certain condition on a fixed point of the equation. If such a condition is not satisfied, there exist solutions that are rational in an exponential function.
Mathematics Subject Classification ID: 39A45
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 6073763
zbMATH Keywords: discrete Painlevé equation
zbMATH Keywords: rational solutions
zbMATH Keywords: difference Painlevé equations
zbMATH Keywords: non-autonomous cases
zbMATH Keywords: auto-Bäcklund transformation
zbMATH Keywords: autonomous cases
reviewed by: Ahmed Hegazi
MaRDI profile type: Publication
OpenAlex ID: W2060007591
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DOI: 10.3836/TJM/1342701346
description: scientific article; zbMATH DE number 6073763