Scattering of Topological Solitons on Barriers and Holes in Two \lambda \phi^4 Models

TL;DR

This paper investigates how topological solitons scatter when encountering barriers and holes in one-dimensional  models, using numerical simulations and analytical methods to understand the effects of obstructions characterized by a potential parameter.

Contribution

It introduces two models with  potentials incorporating obstructions via a potential parameter, analyzing soliton scattering in these settings.

Findings

Solitons exhibit distinct scattering behaviors depending on barrier/hole parameters.

The potential parameter significantly influences soliton transmission and reflection.

Analytical and numerical results agree on key scattering phenomena.

Abstract

We present results of our studies of various scattering properties of topological solitons on obstructions in the form of holes and barriers in 1+1 dimensions. Our results are based on two models involving a \phi^4 potential. The obstructions are characterised by a potential parameter, \lambda which has a non-zero value in a certain region of space and zero elsewhere. In the first model the potential parameter is included in the potential and in the second model the potential parameter is included in the metric. Our results are based on numerical simulations and analytical considerations.