Caudrelier, V and Kundu, A (2015) A multisymplectic approach to defects in integrable classical field theory. Journal of High Energy Physics, 2015 (2). ISSN 1126-6708
Abstract
We introduce the concept of multisymplectic formalism, familiar in covariant field theory, for the study of integrable defects in 1 + 1 classical field theory. The main idea is the coexistence of two Poisson brackets, one for each spacetime coordinate. The Poisson bracket corresponding to the time coordinate is the usual one describing the time evolution of the system. Taking the nonlinear Schrödinger (NLS) equation as an example, we introduce the new bracket associated to the space coordinate. We show that, in the absence of any defect, the two brackets yield completely equivalent Hamiltonian descriptions of the model. However, in the presence of a defect described by a frozen Bäcklund transformation, the advantage of using the new bracket becomes evident. It allows us to reinterpret the defect conditions as canonical transformations. As a consequence, we are also able to implement the method of the classical r matrix and to prove Liouville integrability of the system with such a defect. The use of the new Poisson bracket completely bypasses all the known problems associated with the presence of a defect in the discussion of Liouville integrability. A by-product of the approach is the reinterpretation of the defect Lagrangian used in the Lagrangian description of integrable defects as the generating function 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: | © The Author(s) 2015. Co-published with JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0. |
Keywords: | Integrable Field Theories; Integrable Hierarchies |
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: | 14 Feb 2017 10:47 |
Last Modified: | 23 Jun 2023 22:18 |
Published Version: | https://dx.doi.org/10.1007/JHEP02(2015)088 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/JHEP02(2015)088 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108999 |