Toroidal Solitons in Nicole-type Models

TL;DR

This paper introduces a family of modified Nicole models that admit explicit toroidal solitons with non-trivial Hopf index, revealing new topological solutions with unique energy-charge relations.

Contribution

It presents a novel family of Nicole models with explicit toroidal solitons and analyzes their energy and topological properties, differing from standard formulas.

Findings

Existence of explicit toroidal solitons with non-trivial Hopf index.

Energy-charge relation differs from the Vakulenko-Kapitansky formula.

Solitons resemble eikonal knots.

Abstract

A family of modified Nicole models is introduced. We show that for particular members of the family a topological soliton with a non-trivial value of the Hopf index exists. The form of the solitons as well as their energy and topological charge is explicitly found. They appear to be identical as the so-called eikonal knots. The relation between energy and topological charge of the solution is also presented. Quite interesting it seems to differ drastically from the standard Vakulenko-Kapitansky formula.