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.
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Van Gorder, R.A. Integrable stationary solution for the fully nonlinear local induction equation describing the motion of a vortex filament. Theor. Comput. Fluid Dyn. 26, 591–594 (2012). https://doi.org/10.1007/s00162-011-0244-8
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DOI: https://doi.org/10.1007/s00162-011-0244-8