On the Lagrangian Structure of Integrable Quad-Equations

@inproceedings{Bobenko2010OnTL,
title={On the Lagrangian Structure of Integrable Quad-Equations},
author={Alexander I. Bobenko and Yuri B. Suris},
year={2010}
}

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… CONTINUE READING