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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 1, Pages 23–49
DOI: https://doi.org/10.4213/tmf6624 (Mi tmf6624) 		 
This article is cited in 37 scientific papers (total in 37 papers)

Recursion operators, conservation laws, and integrability conditions for difference equations

A. V. Mikhailova, J. P. Wangb, P. Xenitidisa

a Applied Mathematics Department, University of Leeds, UK
b School of Mathematics and Statistics, University of Kent, UK
Full-text PDF (600 kB) Citations (37)
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DOI: https://doi.org/10.4213/tmf6624
Abstract: We attempt to propose an algebraic approach to the theory of integrable difference equations. We define the concept of a recursion operator for difference equations and show that it generates an infinite sequence of symmetries and canonical conservation laws for a difference equation. As in the case of partial differential equations, these canonical densities can serve as integrability conditions for difference equations. We obtain the recursion operators for the Viallet equation and all the Adler–Bobenko–Suris equations.
Keywords: difference equation, integrability, integrability condition, symmetry, conservation law, recursion operator.
Received: 15.11.2010
English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 1, Pages 421–443
DOI: https://doi.org/10.1007/s11232-011-0033-y
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Mikhailov, J. P. Wang, P. Xenitidis, “Recursion operators, conservation laws, and integrability conditions for difference equations”, TMF, 167:1 (2011), 23–49; Theoret. and Math. Phys., 167:1 (2011), 421–443
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v167/i1/p23
    • This publication is cited in the following 37 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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