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Multisymplectic approach to integrable defects in the sine-Gordon model

Caudrelier, V. (2015). Multisymplectic approach to integrable defects in the sine-Gordon model. Journal of Physics A: Mathematical and Theoretical, 48, 195203. doi: 10.1088/1751-8113/48/19/195203


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 B\"acklund 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.

Publication Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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