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.
Vortex dynamics Vortex filament Local induction equation Stationary solution
Shivamoggi B.K., van Heijst G.J.F.: Motion of a vortex filament in the local induction approximation: Reformulation of the Da Rios-Betchov equations in the extrinsic filament coordinate space. Phys. Lett. A 374, 1742 (2010)MATHCrossRefGoogle Scholar