Casorati determinant solutions for the discrete Painlevé III equation

Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

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
Volume36
Issue number8
DOIs
Publication statusPublished - Jan 1 1995

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Bessel functions
Bessel Functions
determinants
Determinant
Variable Transformation
entry
analogs
formalism
Analogue

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Casorati determinant solutions for the discrete Painlevé III equation. / Kajiwara, Kenji; Ohta, Yasuhiro; Satsuma, Junkichi.

In: Journal of Mathematical Physics, Vol. 36, No. 8, 01.01.1995, p. 4162-4174.

Research output: Contribution to journalArticle

Kajiwara, Kenji ; Ohta, Yasuhiro ; Satsuma, Junkichi. / Casorati determinant solutions for the discrete Painlevé III equation. In: Journal of Mathematical Physics. 1995 ; Vol. 36, No. 8. pp. 4162-4174.
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