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

Arthur, Robert and Dorey, Patrick and Parini, Robert (2016) 'Breaking integrability at the boundary : the sine-Gordon model with Robin boundary conditions.', Journal of physics A: mathematical and theoretical., 49 (16). p. 165205.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher 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
Date accepted:08 February 2016
Date deposited:14 June 2016
Date of first online publication:17 March 2016
Date first made open access:17 March 2017

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