Constructing solutions to the ultradiscrete Painlevé equations

D. Takahashi, T. Tokihiro, B. Grammaticos, Y. Ohta, A. Ramani

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31 Citations (Scopus)

Abstract

We investigate the nature of particular solutions to the ultradiscrete Painlevé equations. We start by analysing the autonomous limit and show that the equations possess an explicit invariant which leads naturally to the ultradiscrete analogue of elliptic functions. For the ultradiscrete Painlevé equations II and III we present special solutions reminiscent of the Casorati determinant ones which exist in the continuous and discrete cases. Finally we analyse the discrete Painlevé equation I and show how it contains both the continuous and the ultradiscrete ones as particular limits.

Original languageEnglish
Pages (from-to)7953-7966
Number of pages14
JournalJournal of Physics A: Mathematical and General
Volume30
Issue number22
DOIs
Publication statusPublished - 1997 Nov 21

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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