Casorati determinant solutions for the discrete Painlevé III equation

Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel functions. Moreover, based on the observation that these discrete Bessel functions are transformed to the q-Bessel functions by a simple variable transformation, we present a q-difference analog of the Painlevé III equation.

Original languageEnglish
Pages (from-to)4162-4174
Number of pages13
JournalJournal of Mathematical Physics
Issue number8
Publication statusPublished - 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Casorati determinant solutions for the discrete Painlevé III equation'. Together they form a unique fingerprint.

Cite this