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Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions

Arthur, Robert; Dorey, Patrick; Parini, Robert

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Authors

Robert Arthur

Robert Parini



Abstract

We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering problem associated with the inverse scattering method. We find that an antikink may be reflected into various combinations of an antikink, a kink, and one or more breathers, depending on the values of the initial antikink velocity and a parameter associated with the boundary condition. In addition we observe regions with an intricate resonance structure arising from the creation of an intermediate breather whose recollision with the boundary is highly dependent on the breather phase.

Citation

Arthur, R., Dorey, P., & Parini, R. (2016). Breaking integrability at the boundary: the sine-Gordon model with Robin boundary conditions. Journal of Physics A: Mathematical and Theoretical, 49(16), Article 165205. https://doi.org/10.1088/1751-8113/49/16/165205

Journal Article Type Article
Acceptance Date Feb 8, 2016
Online Publication Date Mar 17, 2016
Publication Date Mar 17, 2016
Deposit Date Jun 10, 2016
Publicly Available Date Mar 29, 2024
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 49
Issue 16
Article Number 165205
DOI https://doi.org/10.1088/1751-8113/49/16/165205
Related Public URLs https://arxiv.org/abs/1509.08448

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Copyright Statement
This is an author-created, un-copyedited version of an article published in Journal of physics A: mathematical and theoretical. IOP Publishing Ltd 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 10.1088/1751-8113/49/16/165205





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