标题： 关于三维一致的非对称四边形方程组的拉格朗日结构 显示英文标题

标题： On the Lagrangian structure of 3D consistent systems of asymmetric quad-equations

摘要： 近期，第一作者对具有四面体性质的三维一致的六元二次曲面方程组进行了分类；发现了若干新的非对称六元组。 由于三维一致性，这些六元组可以扩展为定义在 Z^m 上的离散可积系统。 我们建立了这一类离散可积系统的拉格朗日结构以及作用量泛函的翻转不变性，该类系统涉及的部分双二次型是非退化的，而另一些则是退化的。 这一类系统涵盖了上述提到的一些新型系统。 显示英文摘要

摘要： Recently, the first-named author gave a classification of 3D consistent 6-tuples of quad-equations with the tetrahedron property; several novel asymmetric 6-tuples have been found. Due to 3D consistency, these 6-tuples can be extended to discrete integrable systems on Z^m. We establish Lagrangian structures and flip-invariance of the action functional for the class of discrete integrable systems involving equations for which some of the biquadratics are non-degenerate and some are degenerate. This class covers, among others, some of the above mentioned novel systems.