To be or knot to be?
Richard A. Battye, Paul M. Sutcliffe

TL;DR
This paper explores the existence and stability of knotted soliton solutions in a three-dimensional classical field theory, revealing a variety of stable configurations like toroids, links, and knots through analytical and numerical methods.
Contribution
It extends previous work by demonstrating a wide range of stable knotted and linked solitons for charges 1 to 8 using advanced analytical and numerical techniques.
Findings
Stable toroidal solitons with twists identified
Linked loops and knots observed as stable solutions
Reconnection of string-like segments enables diverse phenomena
Abstract
It has been suggested recently that knots might exist as stable soliton solutions in a simple three-dimensional classical field theory, opening up a wide range of possible applications in physics and beyond. We have re-examined and extended this work in some detail using a combination of analytic approximations and sophisticated numerical algorithms. For charges between one and eight, we find solutions which exhibit a rich and spectacular variety of phenomena, including stable toroidal solitons with twists, linked loops and also knots. The physical process which allows for this variety is the reconnection of string-like segments.
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