Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions

Yang Shi, Nalini Joshi

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper, we present a new method of deducing infinite sequences of exact solutions of q-discrete Painleve equations by using their associated linear problems. The specific equation we consider in this paper is a q-discrete version of the second Painleve equation (q-PII) with affine Weyl group symmetry of type (A2 + A1)(1). We show, for the first time, how to use the q-discrete linear problem associated with q-PII to find an infinite sequence of exact rational solutions and also show how to find their representation as determinants by using the linear problem. The method, while demonstrated for q-PII here, is also applicable to other discrete Painlevé equations.

Original languageEnglish
Pages (from-to)3443-3468
Number of pages26
JournalPROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume467
Issue number2136
DOIs
Publication statusPublished - 8 Dec 2011
Externally publishedYes

Keywords

  • q-discrete
  • Painlevé equations
  • discrete equations
  • Iso-monodeomy deformation
  • Painlevé
  • Equations
  • Special solutions

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