Mikhailov, AV, Wang, JP and Xenitidis, P (2011) Cosymmetries and Nijenhuis recursion operators for difference equations. Nonlinearity, 24 (7). 2079 - 2097. ISSN 0951-7715
Abstract
In this paper we discuss the concept of cosymmetries and co-recursion operators for difference equations and present a co-recursion operator for the Viallet equation. We also discover a new type of factorization for the recursion operators of difference equations. This factorization enables us to give an elegant proof that the pseudo-difference operator presented in Mikhailov et al 2011 Theor. Math. Phys. 167 421–43 is a recursion operator for the Viallet equation. Moreover, we show that the operator is Nijenhuis and thus generates infinitely many commuting local symmetries. The recursion operator and its factorization into Hamiltonian and symplectic operators have natural applications to Yamilov's discretization of the Krichever–Novikov equation.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2011, IOP Publishing. This is an author produced version of a paper published in Nonlinearity. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Integrable sytems; hereditary symmetries; evolution-equations; classification; transformations |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Sep 2013 11:42 |
Last Modified: | 16 Sep 2016 14:27 |
Published Version: | http://dx.doi.org/10.1088/0951-7715/24/7/009 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/0951-7715/24/7/009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:75293 |