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)
(KAR id:16285)

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. (Contact us about this Publication) | |

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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Engineering and Digital Arts |

Depositing User: | Elizabeth Mansfield |

Date Deposited: | 03 Apr 2009 17:35 UTC |

Last Modified: | 16 Feb 2021 12:27 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/16285 (The current URI for this page, for reference purposes) |

Clarkson, Peter: | https://orcid.org/0000-0002-8777-5284 |

Mansfield, Elizabeth L.: | https://orcid.org/0000-0002-6778-2241 |

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