Scattering of sine-Gordon Breathers on Potential Wells

TL;DR

This paper investigates how sine-Gordon breathers interact with potential wells, revealing complex behaviors such as transmission, trapping, bouncing, and splitting into kink-antikink pairs depending on multiple parameters.

Contribution

It provides a detailed analysis of breather scattering on potential wells, highlighting the dependence on phase, well dimensions, and initial conditions, which was not thoroughly explored before.

Findings

Breathers can pass through, be trapped, or bounce back from the well.

Splitting into kink-antikink pairs occurs upon interaction with the well.

The outcome depends on frequency, speed, phase, and well parameters.

Abstract

We analyse the scattering of sine-Gordon breathers on a square potential well. We show that the scattering process depends not only on the vibration frequency of the breather and its incoming speed but also on its phase as well as the depth and width of the well. We show that the breather can pass through the well and exit with a speed different, sometime larger, from the initial one. It can also be trapped and very slowly decay inside the well or bounce out of the well and go back to where it came from. We also show that the breather can split into a kink and an anti-kink pair when it hits the well.