Soliton on a vortex filament

A vortex filament is said to be a very thin vortex tube. Vortex tubes are structural constituents of turbulence in a fluid. We see the microscopic structure of aether as an ideal fluid pierced in all directions by straight thin vortex tubes. Historically this system is referred to as the vortex sponge. A kink on a straight vortex filament will be taken as a model of a particle.

Abstract. A small amplitude helical waves spreading along an unstretchable vortex filament is shown to obey the linear Schroedinger equation. Taking into account elastic properties of the filament leads to the Klein-Gordon equation.

Abstract.