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Continuous symmetric reductions of the Adler–Bobenko–Suris equations

Tsoubelis, D., Xenitidis, Pavlos (2009) Continuous symmetric reductions of the Adler–Bobenko–Suris equations. Journal of Physics A: Mathematical and Theoretical, 42 (16). p. 165203. ISSN 1751-8113. (doi:10.1088/1751-8113/42/16/165203) (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)

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://doi.org/10.1088/1751-8113/42/16/165203

Abstract

Continuously symmetric solutions of the Adler–Bobenko–Suris class of discrete integrable equations are presented. Initially defined by their invariance under the action of both of the extended three-point generalized symmetries admitted by the corresponding equations, these solutions are shown to be determined by an integrable system of partial differential equations. The connection of this system to the Nijhoff–Hone–Joshi 'generating partial differential equations' is established and an auto-Bäcklund transformation and a Lax pair for it are constructed. Applied to the H1 and Q1?=0 members of the Adler–Bobenko–Suris family, the method of continuously symmetric reductions yields explicit solutions determined by the Painlevé trancendents.

Item Type: Article
DOI/Identification number: 10.1088/1751-8113/42/16/165203
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Pavlos Xenitidis
Date Deposited: 07 Aug 2015 15:15 UTC
Last Modified: 29 May 2019 15:53 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/50070 (The current URI for this page, for reference purposes)
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