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Deautonomizations of integrable equations and their reductions

Xenitidis, Pavlos (2018) Deautonomizations of integrable equations and their reductions. Journal of Integrable Systems, 3 (1). ISSN 2058-5985. E-ISSN 2058-5985. (doi:10.1093/integr/xyy009)

Abstract

We present a deautonomization procedure for partial difference and differential-difference equations (with the latter defining symmetries of the former) which uses the integrability conditions as integrability detector. This procedure is applied to Hirota’s Korteweg–de Vries and all the ABS equations and leads to non-autonomous equations and their non-autonomous generalized symmetries of order two, all of which depend on arbitrary periodic functions and are related to the same two-quad equation and its symmetries. We show how reductions of the derived differential-difference equations lead to alternating QRT maps, and periodic reductions of the difference equations result to non-autonomous maps and discrete Painlevé type equations.

Item Type: Article
DOI/Identification number: 10.1093/integr/xyy009
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Pavlos Xenitidis
Date Deposited: 02 Jul 2018 10:27 UTC
Last Modified: 29 May 2019 20:42 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/67548 (The current URI for this page, for reference purposes)
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