# What is integrability of discrete variational systems?

@article{Boll2014WhatII, title={What is integrability of discrete variational systems?}, author={R. Boll and M. Petrera and Y. Suris}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2014}, volume={470} }

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries… Expand

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Discrete Pluriharmonic Functions as Solutions of Linear Pluri-Lagrangian Systems

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Quantum Variational Principle and quantum multiform structure: the case of quadratic Lagrangians

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Variational symmetries and pluri-Lagrangian systems in classical mechanics

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Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Relativistic Toda-type systems

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Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs

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