On the relation between the continuous and discrete Painleve equations

Clarkson, Peter, Mansfield, Elizabeth L., Webster, Helen N. (2000) On the relation between the continuous and discrete Painleve equations. Theoretical and Mathematical Physics, 122 (1). pp. 1-16. ISSN 0040-5779. (doi:10.1007/BF02551165) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1007/BF02551165

Abstract

A method for deriving difference equations (the discrete Painleve' equations in particular) from the Backlund transformations of the continuous Painleve' equations is discussed. This technique can be used to derive several of the known discrete Painleve' equations (in particular, the first and second discrete Painleve equations and some of their alternative versions). The Painleve' equations possess hierarchies of rational solutions and one-parameter families of solutions expressible in terms of the classical special functions for special values of the parameters. Hence, the aforementioned relations can be used to generate hierarchies of exact solutions for the associated discrete Painleve' equations. Exact solutions of the Painleve equations simultaneously satisfy both a differential equation and a difference equation, analogously to the special functions.

Item Type: Article
DOI/Identification number: 10.1007/BF02551165
Uncontrolled keywords: Difference Equation, Continuous Limit, Rational Solution, Discrete Equation, Mathematical Science Research Institute
Subjects: Q Science > QC Physics
Divisions: Faculties > Sciences > School of Engineering and Digital Arts
Depositing User: Elizabeth L Mansfield
Date Deposited: 03 Apr 2009 17:35 UTC
Last Modified: 07 Jun 2019 10:58 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/16285 (The current URI for this page, for reference purposes)
Mansfield, Elizabeth L.: https://orcid.org/0000-0002-6778-2241
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