Translator Disclaimer
June 2012 Rational Solutions of Difference Painlevé Equations
Shun SHIMOMURA
Tokyo J. Math. 35(1): 85-95 (June 2012). DOI: 10.3836/tjm/1342701346

Abstract

We capture all the rational solutions of some difference Painlevé equations of P$_{\mathrm{I}}$ and P$_{\mathrm{II}}$ types. For non-autonomous cases, it is shown that all the rational solutions of the difference P$_{\mathrm{II}}$ are ones generated by successive application of auto-Bäcklund transformations to the seed solution vanishing identically, and that the other equations of P$_{\mathrm{I}}$ type admit no rational solutions. For autonomous cases, all the 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.

Citation

Download Citation

Shun SHIMOMURA. "Rational Solutions of Difference Painlevé Equations." Tokyo J. Math. 35 (1) 85 - 95, June 2012. https://doi.org/10.3836/tjm/1342701346

Information

Published: June 2012
First available in Project Euclid: 19 July 2012

zbMATH: 1259.39014
MathSciNet: MR2977447
Digital Object Identifier: 10.3836/tjm/1342701346

Subjects:
Primary: 39A45
Secondary: 34M55, 39A12

Rights: Copyright © 2012 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.35 • No. 1 • June 2012
Back to Top