论文标题
双曲线类型半污垢方程的广义对称性和可集成性条件
Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations
论文作者
论文摘要
在文章中，从整合性观点研究了双曲线类型的差异差异（半差异）晶格。更准确地说，我们集中于一种构建广义对称性的方法。这种可集成的晶格允许对应于离散和连续的独立变量$ n $和$ x $的两个概括对称性的两个层次结构。与$ n $方向相对应的对称性以或多或少的标准方式构建时，在构造其他形式的对称性时，我们遇到了解决功能方程的问题。我们已经证明，要使用该方程式处理，可以有效地使用半混凝土模型的特征性lie-rinehart代数的概念。基于此观察结果，我们提出了一种用于整合半凝结晶格的分类方法。这项工作的有趣结果之一是一个可集成方程的新示例，该方程是Tzizeica方程的半差异类似物。此类例子以前不知道。
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable lattices admit two hierarchies of generalized symmetries corresponding to the discrete and continuous independent variables $n$ and $x$. Symmetries corresponding to the direction of $n$ are constructed in a more or less standard way while when constructing symmetries of the other form we meet a problem of solving a functional equation. We have shown that to handle with this equation one can effectively use the concept of characteristic Lie-Rinehart algebras of semi-discrete models. Based on this observation, we have proposed a classification method for integrable semi-discrete lattices. One of the interesting results of this work is a new example of an integrable equation, which is a semi-discrete analogue of the Tzizeica equation. Such examples were not previously known.
