Knotted solutions, from electromagnetism to fluid dynamics

Abstract

Knotted solutions to electromagnetism and fluid dynamics are investigated, based on relations we find between the two subjects. We can write fluid dynamics in electromagnetism language, but only on an initial surface, or for linear perturbations, and we use this map to find knotted fluid solutions, as well as new electromagnetic solutions. We find that knotted solutions of Maxwell electromagnetism are also solutions of more general nonlinear theories, like Born-Infeld, and including ones which contain quantum corrections from couplings with other modes, like Euler-Heisenberg and string theory DBI. Null configurations in electromagnetism can be described as a null pressureless fluid, and from this map we can find null fluid knotted solutions. A type of nonrelativistic reduction of the relativistic fluid equations is described, which allows us to find also solutions of the (nonrelativistic) Euler's equations.

36 pages, 3 figures

References in corpus (3)

• The quantum mechanics of perfect fluids
• New knotted solutions of Maxwell's equations
• Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics

Cited by in corpus (7)

• Scalar field as a null dust
• On the existence of the field line solutions of the Einstein-Maxwell equations
• Finsler Geometries from Topological Electromagnetism
• Nonlinear dynamics of a charged particle in a strong non-null knot wave background
• Hopfion solutions in gravity and a null fluid/gravity conjecture
• Gravitoelectromagnetic knot fields
• Coupling ModMax theory precursor with scalars, and BIon-type solutions