Second order integrability conditions for difference equations: an integrable equation (Q464330)

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.