Sleigh, D orcid.org/0000-0001-6499-3951, Nijhoff, F and Caudrelier, V orcid.org/0000-0003-0129-6758 (2020) Variational symmetries and Lagrangian multiforms. Letters in Mathematical Physics, 110 (4). pp. 805-826. ISSN 0377-9017
Abstract
By considering the closure property of a Lagrangian multiform as a conservation law, we use Noether’s theorem to show that every variational symmetry of a Lagrangian leads to a Lagrangian multiform. In doing so, we provide a systematic method for constructing Lagrangian multiforms for which the closure property and the multiform Euler–Lagrange (EL) both hold. We present three examples, including the first known example of a continuous Lagrangian 3-form: a multiform for the Kadomtsev–Petviashvili equation. We also present a new proof of the multiform EL equations for a Lagrangian k-form for arbitrary k.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Nature B.V. 2019. This is an author produced version of an article published in Letters in Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Integrable systems; Variational principle; Variational symmetries; Lagrangian multiforms |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Nov 2019 14:00 |
Last Modified: | 18 Dec 2020 05:56 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s11005-019-01240-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:153145 |