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arXiv · 1108.0016

On the Lagrangian structure of 3D consistent systems of asymmetric quad-equations

Raphael Boll·Yuri B. Suris
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Abstract

Recently, the first-named author gave a classification of 3D consistent 6-tuples of quad-equations with the tetrahedron property; several novel asymmetric 6-tuples have been found. Due to 3D consistency, these 6-tuples can be extended to discrete integrable systems on Z^m. We establish Lagrangian structures and flip-invariance of the action functional for the class of discrete integrable systems involving equations for which some of the biquadratics are non-degenerate and some are degenerate. This class covers, among others, some of the above mentioned novel systems.

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Raphael Boll, Yuri B. Suris. 2011-07-29. On the Lagrangian structure of 3D consistent systems of asymmetric quad-equations. https://doi.org/10.1088/1751-8113/45/11/115201

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