Scattering of Sine-Gordon kinks on potential wells

TL;DR

This paper investigates how Sine-Gordon kinks scatter off potential wells, revealing energy radiation, trapping, transmission, and unexpected reflections, modeled through simple standing wave interactions.

Contribution

It introduces models that explain the scattering behavior of Sine-Gordon kinks on potential wells, highlighting radiation effects and unexpected reflections.

Findings

Kinks radiate energy when in the well, leading to trapping or transmission.

Interaction with radiation can cause unexpected reflections.

Simple models with standing waves capture key scattering features.

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 $\cos(\phi)-1$ 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.