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On the Lagrangian structure of integrable quad-equations

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arxiv 0912.2464 v2 pith:PEFLNYKV submitted 2009-12-14 nlin.SI math-phmath.MP

Alexander I. Bobenko , Yuri B. Suris (TU Berlin) This is my paper · ORCID
classification nlin.SImath-phmath.MP
keywords integrableflipinvariancequad-equationsactionbazhanovblockbuilding
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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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  1. Discrete Lagrangian Multiforms for ABS Equations I: Quad Equations

    nlin.SI 2025-01 conditional novelty 7.0 of 10

    Trident Lagrangian 2-forms with integer-valued branch-tracking fields have corner equations equivalent to the ABS quad equations and restore almost-closure.

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