Interaction of topological solitons with defects: using a nontrivial metric

TL;DR

This paper investigates how sine-Gordon solitons interact with potential defects by incorporating a nontrivial metric, revealing classical and non-classical behaviors such as trapping and radiation emission.

Contribution

It introduces a novel approach using a nontrivial metric to study soliton-defect interactions, highlighting differences between barrier and well potentials.

Findings

Soliton-barrier interactions are fully classical.

Soliton-well interactions exhibit non-classical trapping.

Low-velocity solitons in wells emit radiation.

Abstract

By including potential into the flat metric, we study interaction of sine-Gordon soliton with potentials. We will show numerically that while the soliton-barrier system shows fully classical behaviour, the soliton-well system demonstrates non-classical behaviour. In particular, solitons with low velocities are trapped in the well and emit energy radiation.