Caudrelier, V (2015) Multisymplectic approach to integrable defects in the sine-Gordon model. Journal of Physics A: Mathematical and Theoretical, 48 (19). pp. 1-23. ISSN 1751-8113
Abstract
Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key ingredient is the introduction of a second Poisson bracket in the theory that allows for a Hamiltonian description of the model that is completely equivalent to the standard one, in the absence of a defect. In the presence of a defect described by frozen Bäcklund transformations, our approach based on the new bracket unifies the various tools used so far to attack the problem. It also gets rid of the known issues related to the evaluation of the Poisson brackets of the defect matrix which involve fields at coinciding space point (the location of the defect). The original Lagrangian approach also finds a nice reinterpretation in terms of the canonical transformation representing the defect conditions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2015, IOP Publishing. This is an author produced version of a paper published in Journal of Physics A: Mathematical and Theoretical. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | sine-Gordon model, integrable defect, Liouville integrability, |
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: | 10 Feb 2017 16:00 |
Last Modified: | 10 Feb 2017 16:00 |
Published Version: | https://dx.doi.org/10.1088/1751-8113/48/19/195203 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1751-8113/48/19/195203 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108997 |