Second Order Integrability Conditions for Difference Equations: An Integrable Equation
Second Order Integrability Conditions for Difference Equations: An Integrable Equation
复制标题
差分方程的二阶可积条件：可积方程
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
P. Xenitidis
中科院分区：
文献类型：
--
作者：
A. Mikhailov;P. Xenitidis
给出了含有二阶形式递归算子的差分方程的可积性条件，讨论了对称性和正则守恒律的推导。在一般情况下，其中一些条件产生非局部守恒律。提出了一个满足二阶可积条件的新的可积方程，并通过构造对称性、守恒律和3 × 3 Lax表示，证明了它的可积性.最后，通过该方程的对称性与Bogoyavlensky格的关系，得到了一个可积的非对称四元方程和一对相容的差分方程。
Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws are discussed. In a generic case, some of these conditions yield nonlocal conservation laws. A new integrable equation satisfying the second order integrability conditions is presented and its integrability is established by the construction of symmetries, conservation laws and a 3 × 3 Lax representation. Finally, via the relation of the symmetries of this equation to the Bogoyavlensky lattice, an integrable asymmetric quad equation and a consistent pair of difference equations are derived.