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Special Solutions for Discrete Painlevé Equations

  • K.M. Tamizhmani
  • T. Tamizhmani
  • B. Grammaticos
  • A. Ramani
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 644)

Abstract

We construct special solutions for the discrete Painlevé equations. We start with a review of the corresponding solutions in the case of the continuous Painlevé equations and then proceed to construct the solutions in the discrete case. We show how, starting from an elementary, seed solution, one can use the auto-Bäcklund transformations in order to build iteratively ‘higher’ solutions. Using the bilinear formalism we show that the τ-functions for these ‘higher’ solutions can be cast into the form of Casorati determinants.

Keywords

Riccati Equation Continuous Limit Special Solution Rational Solution Incomplete Gamma Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  • K.M. Tamizhmani
    • 1
  • T. Tamizhmani
    • 2
  • B. Grammaticos
    • 3
  • A. Ramani
    • 4
  1. 1.Departement of Mathematics, Pondicherry University, Kalapet, Pondicherry 605014India
  2. 2.Department of Mathematics, Kanchi Mamunivar Centre for Postgraduate Studies, Pondicherry 605008India
  3. 3.GMPIB, Université Paris VII, Tour 24-14, 5e étage, case 7021, 75251 ParisFrance
  4. 4.CPT, Ecole Polytechnique, CNRS, UMR 7644, 91128 Palaiseau, France

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