On the Lagrangian Structure of Integrable Quad-Equations |
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Authors: | Alexander I Bobenko and Yuri B Suris |
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Institution: | 1.Institut für Mathematik, MA 8-3,TU Berlin,Berlin,Germany;2.Institut für Mathematik, MA 7-2,TU Berlin,Berlin,Germany |
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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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Keywords: | |
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