Caudrelier, V. orcid.org/0000-0003-0129-6758, Singh, A.A. and Vicedo, B. (2024) Lagrangian Multiform for Cyclotomic Gaudin Models. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 20. ISSN 1815-0659
Abstract
We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoint orbits. This provides the first example of a Lagrangian multiform for an integrable hierarchy whose classical r -matrix is non-skew-symmetric and spectral parameter-dependent. As an important by-product of the construction, we obtain a Lagrangian multiform for the periodic Toda chain by choosing an appropriate realisation of the cyclotomic Gaudin Lax matrix. This fills a gap in the landscape of Toda models as only the open and infinite chains had been previously cast into the Lagrangian multiform framework. A slightly different choice of realisation produces the so-called discrete self-trapping (DST) model. We demonstrate the versatility of the framework by coupling the periodic Toda chain with the DST model and by obtaining a Lagrangian multiform for the corresponding integrable hierarchy.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Authors. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY-SA 4.0). |
Keywords: | Lagrangian multiforms; integrable systems; classical r-matrix; Gaudin models |
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: | 20 Nov 2024 13:50 |
Last Modified: | 20 Nov 2024 13:50 |
Status: | Published online |
Publisher: | National Academy of Science of Ukraine |
Identification Number: | 10.3842/SIGMA.2024.100 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:219867 |
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