Knots and the Maxwell Equations

Abstract

In this chapter, we review the Rañada field line solutions of Maxwell's equations in the vacuum, which describe a topologically non-trivial electromagnetic field, as well as their relation with the knot theory. Also, we present a generalization of these solutions to the non-linear electrodynamics recently published in the literature.

Published in An Essential Guide to Maxwell's Equations, Editor Casey Erickson, Nova Science Publishers, https://novapublishers.com/shop/an-essential-guide-to-maxwells-equations/

References in corpus (10)

• Knotted solutions, from electromagnetism to fluid dynamics
• Weaving knotted vector fields with tunable helicity
• Classification of Electromagnetic and Gravitational Hopfions by Algebraic Type
• Self-organizing Knotted Magnetic Structures in Plasma
• Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics
• A new construction of rational electromagnetic knots
• Knotted optical vortices in exact solutions to Maxwell's equations
• On rational electromagnetic fields
• On the existence of the field line solutions of the Einstein-Maxwell equations
• Hopfion solutions in gravity and a null fluid/gravity conjecture