Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics

Abstract

We examine knotted solutions, the most simple of which is the "Hopfion", from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.

5 pages plus references; references added

References in corpus (2)

• The quantum mechanics of perfect fluids
• New knotted solutions of Maxwell's equations

Cited by in corpus (8)

• Knotted solutions, from electromagnetism to fluid dynamics
• On the existence of the field line solutions of the Einstein-Maxwell equations
• Nonlinear dynamics of a charged particle in a strong non-null knot wave background
• Finsler Geometries from Topological Electromagnetism
• Hopfion solutions in gravity and a null fluid/gravity conjecture
• Gravitoelectromagnetic knot fields
• Coupling ModMax theory precursor with scalars, and BIon-type solutions
• Gravity and its wonders: braneworlds and holography