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This article is cited in 24 scientific papers (total in 24 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
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
DOI:
https://doi.org/10.4213/tmf6624
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English version:
Theoretical and Mathematical Physics, 2011, 167:1, 421–443
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Received: 15.11.2010
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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