Rational solutions of difference painlevé equations

Shun Shimomura

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We capture all the rational solutions of some difference Painlevé equations of PI and PII types. For non-autonomous cases, it is shown that all the rational solutions of the difference PII are ones generated by successive application of auto-Bäcklund transformations to the seed solution vanishing identically, and that the other equations of PI 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.

Original languageEnglish
Pages (from-to)85-95
Number of pages11
JournalTokyo Journal of Mathematics
Volume35
Issue number1
DOIs
Publication statusPublished - 2012 Jun

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Rational Solutions
Difference equation
Fixed point

Keywords

  • Difference Painlevé equation
  • Rational solution

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Rational solutions of difference painlevé equations. / Shimomura, Shun.

In: Tokyo Journal of Mathematics, Vol. 35, No. 1, 06.2012, p. 85-95.

Research output: Contribution to journalArticle

Shimomura, Shun. / Rational solutions of difference painlevé equations. In: Tokyo Journal of Mathematics. 2012 ; Vol. 35, No. 1. pp. 85-95.
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