论文标题
在具有非标准对称结构的正方形晶格上修改的一系列可集成离散方程
Modified series of integrable discrete equations on a square lattice with a non-standard symmetry structure
论文作者
论文摘要
在作者最近的一篇论文[TMP，200：1（2019），966--984]中，构建了一系列具有广义对称性非标准结构的正方形晶格上的一系列可集成的离散自主方程。我们通过使用离散的非点转换来构建修改后的系列。我们在离散方程的解决方案上使用不可矛盾的线性变换和不可逆转的不可转化。结果，我们获得了几个新的离散方程式示例，以及它们的广义对称性和主体对称性。构建的广义对称性提供了五点和七点差分方程的新示例以及其主对称性。在离散方程式的情况下，显然是首次考虑使用保护定律构建不可消性的线性变换的方法。
In a recent paper [TMP, 200:1 (2019), 966--984] by the authors, a series of integrable discrete autonomous equations on a square lattice with a non-standard structure of generalized symmetries is constructed. We build modified series by using discrete non-point transformations. We use both non-invertible linearizable transformations and non-point transformations invertible on solutions of the discrete equation. As a result, we get several series of new examples of discrete equations along with their generalized symmetries and master symmetries. The generalized symmetries constructed give new integrable examples of five- and seven-point differential-difference equations together with their master symmetries. In the case of discrete equations, the method of constructing non-invertible linearizable transformations by using conservation laws is considered, apparently, for the first time.
