, Volume 26, Issue 6, pp 591-594
Date: 18 Nov 2011

Integrable stationary solution for the fully nonlinear local induction equation describing the motion of a vortex filament

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Abstract

In this brief communication, we demonstrate an implicit exact stationary solution to the fully nonlinear local induction equation describing the motion of a vortex filament. The solution, which is periodic in the spatial variable, is governed by a second-order nonlinear equation that has two exact first integrals.