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arXiv · 0912.2464

On the Lagrangian structure of integrable quad-equations

Alexander I. Bobenko·Yuri B. Suris
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Abstract

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.

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Alexander I. Bobenko, Yuri B. Suris. 2010-02-21. On the Lagrangian structure of integrable quad-equations. https://doi.org/10.1007/s11005-010-0381-9

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