Sleigh, D, Nijhoff, F and Caudrelier, V orcid.org/0000-0003-0129-6758 (2019) A Variational Approach to Lax Representations. Journal of Geometry and Physics, 142. pp. 66-79. ISSN 0393-0440
Abstract
It is shown that the Zakharov–Mikhailov (ZM) Lagrangian structure for integrable nonlinear equations derived from a general class of Lax pairs possesses a Lagrangian multiform structure in the sense of [8]. We show that, as a consequence of this multiform structure, we can formulate a variational principle for the Lax pair itself, a problem that to our knowledge was never previously considered. As an example, we present an integrable N X N matrix system that contains the AKNS hierarchy, and we exhibit the Lagrangian multiform structure of the scalar AKNS hierarchy by presenting the components corresponding to the first three flows of the hierarchy.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Elsevier B.V. All rights reserved. This is an author produced version of a paper published in Journal of Geometry and Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Lagrangian multiform; Integrable systems; Classical field theory; Variational calculus; Variational principle |
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: | 25 Apr 2019 11:00 |
Last Modified: | 04 Apr 2020 00:38 |
Status: | Published |
Publisher: | Elsevier BV |
Identification Number: | 10.1016/j.geomphys.2019.03.015 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:145317 |