Discretising systematically the Painlevé equations
type: Item
instance of: scholarly article
title: Discretising systematically the Painlevé equations
zbMATH Open document ID: 1217.37059
published in: Physica D
publication date: 2011-03-08T00:00:00Z
review text: Integrable discrete analogues of the Painlevé equations have been constructed by Grammaticos, Ramani, et.\ al.\ some time ago. In the present paper it is shown that this can be done using the systematic discretisation procedure introduced by the authors in [J. Phys. A, Math. Theor. 43, No. 31, Article ID 315203, 15 p. (2010; Zbl 1222.39009)]. This is achieved by applying the discretisation method directly to the Hamiltonian equations of motion which define each Painlevé equation. These are in general of Riccati type (after a simple change of variables).
reviewed by: Johanna Michor
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 5862551
zbMATH Keywords: discretisation
zbMATH Keywords: Painlevé equations
zbMATH Keywords: discrete models
zbMATH Keywords: integrable mappings
author: M. Murata
author: J. Satsuma
author: A. Ramani
author: B. Grammaticos
MaRDI profile type: Publication
full work available at URL: j.physd.2010.09.007
OpenAlex ID: W2015223698
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DOI: 10.1016/J.PHYSD.2010.09.007
description: scientific article; zbMATH DE number 5862551