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

Arthur, Robert; Dorey, Patrick; Parini, Robert

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 17, 2017
• 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
• Public URL: https://durham-repository.worktribe.com/output/1381194
• Related Public URLs: https://arxiv.org/abs/1509.08448