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On the discrete and continuous Miura Chain associated with the Sixth Painlevé Equation

Nijhoff, Frank W., Joshi, Nalini, Hone, Andrew N.W. (2000) On the discrete and continuous Miura Chain associated with the Sixth Painlevé Equation. Physics Letters A, 264 (5). pp. 396-406. ISSN 0375-9601. (doi:10.1016/S0375-9601(99)00764-1)

Abstract

A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or B\"acklund transformations. We describe such a chain for the sixth Painlev\'e equation (\pvi), containing, apart from \pvi itself, a Schwarzian version as well as a second-order second-degree ordinary differential equation (ODE). As a byproduct we derive an auto-B\"acklund transformation, relating two copies of \pvi with different parameters. We also establish the analogous ordinary difference equations in the discrete counterpart of the chain. Such difference equations govern iterations of solutions of \pvi under B\"acklund transformations. Both discrete and continuous equations constitute a larger system which include partial difference equations, differential-difference equations and partial differential equations, all associated with the lattice Korteweg-de Vries equation subject to similarity constraints.

Item Type: Article
DOI/Identification number: 10.1016/S0375-9601(99)00764-1
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew N W Hone
Date Deposited: 21 Jun 2014 23:22 UTC
Last Modified: 29 May 2019 12:42 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/41500 (The current URI for this page, for reference purposes)
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