Ring-shaped exact Hopf solitons

TL;DR

This paper demonstrates the existence of exact Hopf soliton solutions with ring-like structures, contributing to the understanding of topological solitons in field theories.

Contribution

It introduces the first exact solutions of Hopf solitons with ring-shaped structures, advancing the theoretical understanding of topological solitons.

Findings

Exact ring-shaped Hopf soliton solutions are constructed.

These solutions confirm the possibility of stable ring-like topological structures.

The results provide new insights into the topology of solitons.

Abstract

The existence of ring-like structures in exact hopfion solutions is shown.