标题： 关于可积四边形方程的拉格朗日结构 显示英文标题

标题： On the Lagrangian structure of integrable quad-equations

摘要： 在多维格点中作用泛函的翻转不变性这一新概念最近被强调为离散可积系统的关键特征。 翻转不变性已被证明适用于Bazhanov、Mangazeev和Sergeev以及Lobb和Nijhoff的几种特定可积四边形方程的情况。 我们为所有可积四边形方程提供了一个简单且与情况无关的证明。 此外，我们在一个基本四边形内发现了一个关于拉格朗日量的新关系，这似乎是以各种翻转不变性版本的基本构建块。 显示英文摘要

摘要： The new idea of flip invariance of action functionals in multidimensional lattices was recently highlighted as a key feature of discrete integrable systems. Flip invariance was proved for several particular cases of integrable quad-equations by Bazhanov, Mangazeev and Sergeev and by Lobb and Nijhoff. We provide a simple and case-independent proof for all integrable quad-equations. Moreover, we find a new relation for Lagrangians within one elementary quadrilateral which seems to be a fundamental building block of the various versions of flip invariance.