Rational solutions of difference painlevé equations

Shun Shimomura

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number1
Publication statusPublished - 2012 Jun


  • Difference Painlevé equation
  • Rational solution

ASJC Scopus subject areas

  • Mathematics(all)


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