Variational symmetries and pluri-Lagrangian systems

TL;DR

This paper explores the connection between pluri-Lagrangian systems, a concept from integrable systems theory, and classical variational symmetries introduced by Noether, highlighting their theoretical relationship.

Contribution

It establishes a link between modern pluri-Lagrangian systems and classical variational symmetry concepts, enriching the understanding of integrable systems.

Findings

Identifies the relationship between pluri-Lagrangian systems and Noether's variational symmetries

Provides a theoretical framework connecting modern and classical variational principles

Enhances the conceptual understanding of symmetries in integrable systems

Abstract

We analyze the relation of the notion of pluri-Lagrangian systems, which recently emerged in the theory of integrable systems, to the classical notion of variational symmetry, due to E. Noether.