Stability of a Steady Vortex Filament

Abstract

Stability of a steady vortex filament governed by the localized induction equation is investigated by a linear stability theory. It is shown numerically that the solitary-wave-type unclosed filament and some kinds of closed filaments are neutrally stable while all the other closed and unclosed filaments are unstable. Correspondingly, the envelope solitary wave of the nonlinear Schrödinger equation is neutrally stable and all the other travelling wave solutions are unstable.