Static Hopfion solutions of the extended Skyrme-Faddeev model

TL;DR

This paper constructs and numerically analyzes non-axially symmetric static soliton solutions with high topological charges in an extended Skyrme-Faddeev model, revealing a preference for large ring-like configurations.

Contribution

It introduces a new extended Skyrme-Faddeev model with a negative coupling term and finds novel static soliton solutions with high topological charges.

Findings

Solutions include non-axially symmetric configurations.

Large ring-like solutions are favored in the model.

Topological charges up to seven are achieved.

Abstract

We construct non-axially symmetric static soliton solutions, with non-zero topological charges, of an extension of the Skyrme-Faddeev model. The model has an extra quartic-derivative term and we choose its coupling to the Skyrme-term to be negative. We solve the full equations of motion to find numerical solutions with topological charge up to seven and find that the model favours large ring-like solutions.