Title: 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.