Coalescence cascades and special-function solutions for the continuous and discrete Painlevé equations

K. M. Tamizhmani, A. Ramani, B. Grammaticos, K. Kajiwara

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We present a systematization of the special-function type solutions of continuous and discrete Painlevé equations. Our method is to start from PVI and construct its special solutions from the solutions of the hypergeometric equation, and by coalescence obtain the lower Painlevé equations together with their special solutions. In the discrete case we study the 'symmetric', one-component, three-point mapping forms of discrete Painlevé equations starting from d-PV.

Original languageEnglish
Pages (from-to)5799-5810
Number of pages12
JournalJournal of Physics A: Mathematical and General
Volume31
Issue number27
DOIs
Publication statusPublished - Jul 10 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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