Related Experiment Video
Updated: May 16, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Exact solution for the self-induced motion of a vortex filament in the arc-length representation of the local
1Department of Mathematics, University of Central Florida, Orlando, Florida 32816-1364, USA. rav@knights.ucf.edu
Abstract:
We review two formulations of the fully nonlinear local induction equation approximating the self-induced motion of the vortex filament (in the local induction approximation), corresponding to the Cartesian and arc-length coordinate systems. The arc-length representation put forth by Umeki [Theor. Comput. Fluid Dyn. 24, 383 (2010)] results in a type of 1+1 derivative nonlinear Schrödinger (NLS) equation describing the motion of such a vortex filament. We obtain exact stationary solutions to this derivative NLS equation; such exact solutions are a rarity. These solutions are periodic in space and we determine the nonlinear dependence of the period on the amplitude.
Related Concept Videos
Self-Inductance
Consider a circuit connected to an AC source. As the current varies with time, the magnetic flux through the circuit correspondingly changes. Faraday's law tells us that an emf would therefore...
Calculation of Self-inductance
Since the effect of the induced electric field and the back EMF generated depends on the rate of change of current and the self-inductance, the inductance...
Induced Electric Fields: Applications
Motion Of A Charged Particle In A Magnetic Field
Induced Electric Fields
Inductor in an AC Circuit

