Scattering of Sine-Gordon kinks on potential wells

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 $\cos (\varphi )-1$ 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.

arXiv comment14 pages, 12 figures

References in corpus (7)

• Kink dynamics in a novel discrete sine-Gordon system
• Classically integrable field theories with defects
• Stopping Light on a Defect
• Interaction of sine-Gordon kinks with defects: The two-bounce resonance
• Dynamical properties of a Soliton in a Potential Well
• Information transport by sine-Gordon solitons in microtubules
• Purely transmitting integrable defects

Cited by in corpus (9)

• Solvable self-dual impurity models
• Dynamics of multi-kinks in the presence of wells and barriers
• A Mechanical Analog of the Two-bounce Resonance of Solitary Waves: Modeling and Experiment
• Scattering of sine-Gordon Breathers on Potential Wells
• Dynamics of the topological structures in inhomogeneous media
• Critical velocity in kink-defect interaction models: rigorous results
• Q-ball Scattering on Barriers and Holes in 1 and 2 Spatial Dimensions
• Pinned fluxons in a Josephson junction with a finite-length inhomogeneity
• Existence of stationary fronts in a system of two coupled wave equations with spatial inhomogeneity