Second order integrability conditions for difference equations: an integrable equation
type: Item
instance of: scholarly article
title: Second order integrability conditions for difference equations: an integrable equation
zbMATH Open document ID: 1305.39011
author: Alexander V. Mikhailov
author: Pavlos Xenitidis
published in: Letters in Mathematical Physics
publication date: 2014-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1305.4347
review text: By the term ``integrability of a difference equation'' the authors mean that there exists an infinite hierarchy of symmetries. This paper presents such integrability conditions for difference equations admitting a second-order (formal) recursion operator. Moreover, the derivation of symmetries and canonical conservation laws are discussed. Some of these conditions generically yield nonlocal conservation laws. The authors deduce a new integrable equation fulfilling second-order integrability conditions. The latter property is established by constructing symmetries, conservation laws and a \(3\times 3\) Lax representation. By means of the relation of its symmetries to the Bogoyavlensky lattice, an integrable asymmetric quad equation and a consistent pair of difference equations are derived.
Mathematics Subject Classification ID: 39A14
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 70G65
zbMATH DE Number: 6358063
zbMATH Keywords: difference equation
zbMATH Keywords: integrability condition
zbMATH Keywords: recursion operator
zbMATH Keywords: conservation law
zbMATH Keywords: symmetry
zbMATH Keywords: Lax pair
zbMATH Keywords: Bogoyavlensky lattice
reviewed by: Christian Pötzsche
MaRDI profile type: Publication
OpenAlex ID: W3105597154
Wikidata QID: Q61835377
arXiv ID: 1305.4347
cites work: Affine linear and D4symmetric lattice equations: symmetry analysis and reductions
cites work: Classification of integrable equations on quad-graphs. The consistency approach
cites work: Differential–difference equations associated with the fractional Lax operators
cites work: Toward a theory of integrable hyperbolic equations of third order
cites work: Q4663133
cites work: Generalized symmetry classification of discrete equations of a class depending on twelve parameters
cites work: Generalized symmetry integrability test for discrete equations on the square lattice
cites work: Q3974039
cites work: A new recursion operator for Adler's equation in the Viallet form
cites work: Recursion operators, conservation laws, and integrability conditions for difference equations
cites work: Cosymmetries and Nijenhuis recursion operators for difference equations
cites work: Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
cites work: On some class of reductions for the Itoh–Narita–Bogoyavlenskii lattice
cites work: Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice
DOI: 10.1007/S11005-013-0668-8
description: scientific article; zbMATH DE number 6358063