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

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.

21 pp, pdfLaTeX

References in corpus (4)

• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Classification of 3D consistent quad-equations
• On the Lagrangian structure of integrable quad-equations
• On multidimensional consistent systems of asymmetric quad-equations

Cited by in corpus (9)

• What is integrability of discrete variational systems?
• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
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• Integrable quad equations derived from the quantum Yang-Baxter equation
• Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Relativistic Toda-type systems
• Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems
• A Variational Principle for Discrete Integrable Systems
• Integrable Hamiltonian Hierarchies and Lagrangian 1-Forms
• On multidimensional consistent systems of asymmetric quad-equations