Loughborough University
Browse
2021 - EJM - Variational symmetries and pluri-Lagrangian structures.pdf (379.2 kB)

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

Download (379.2 kB)
journal contribution
posted on 2024-01-03, 10:13 authored by Matteo Petrera, Mats VermeerenMats Vermeeren

We investigate the relation between pluri-Lagrangian hierarchies of 2-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings in Petrera and Suris (Nonlinear Math. Phys. 24(suppl. 1):121–145, 2017) for ordinary differential equations. We consider hierarchies of 2-dimensional Lagrangian PDEs (many of which have a natural $$(1\,{+}\,1)$$ ( 1 + 1 ) -dimensional space-time interpretation) and show that if the flow of each PDE is a variational symmetry of all others, then there exists a pluri-Lagrangian 2-form for the hierarchy. The corresponding multi-time Euler–Lagrange equations coincide with the original system supplied with commuting evolutionary flows induced by the variational symmetries.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

European Journal of Mathematics

Volume

7

Issue

2

Pages

741 - 765

Publisher

Springer

Version

  • VoR (Version of Record)

Rights holder

© The Author(s)

Publisher statement

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Acceptance date

2020-10-01

Publication date

2020-11-09

Copyright date

2020

ISSN

2199-675X

eISSN

2199-6768

Language

  • en

Depositor

Dr Mats Vermeeren. Deposit date: 19 December 2023

Usage metrics

    Loughborough Publications

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC