Scattering of Sine-Gordon kinks on potential wells

Piette, B.; Zakrzewski, W.J.

Abstract

We study the scattering properties of sine-Gordon kinks on obstructions in the form of finite size potential 'wells'. We model this by making the coefficient of the cos(phiv) − 1 term in the Lagrangian position dependent. We show that when the kinks find themselves in the well they radiate and then interact with this radiation. As a result of this energy loss, the kinks become trapped for small velocities while at higher velocities they are transmitted with a loss of energy. However, the interaction with the radiation can produce 'unexpected' reflections by the well. We present two simple models which capture the gross features of this behaviour. Both involve standing waves either at the edges of the well or in the well itself.

Citation

Piette, B., & Zakrzewski, W. (2007). Scattering of Sine-Gordon kinks on potential wells. Journal of Physics A: Mathematical and Theoretical, 40(22), 5995-6010. https://doi.org/10.1088/1751-8113/40/22/016

• Journal Article Type: Article
• Publication Date: 2007-06
• Deposit Date: Nov 22, 2010
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 22
• Pages: 5995-6010
• DOI: https://doi.org/10.1088/1751-8113/40/22/016
• Keywords: Nonlinear or nonlocal theories and models, Lagrangian and Hamiltonian approach
• Public URL: https://durham-repository.worktribe.com/output/1515230
• Publisher URL: http://iopscience.iop.org/1751-8121/40/22/016