Abbreviated Journal Title
Phys. Rev. E
SUPERFLUID-HELIUM; EQUATIONS; KNOTS; INVARIANTS; DYNAMICS; SOLITON; WAVES; HE-4; Physics, Fluids & Plasmas; Physics, Mathematical
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 Schrodinger (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.
Physical Review E
Van Gorder, Robert A., "Exact solution for the self-induced motion of a vortex filament in the arc-length representation of the local induction approximation" (2012). Faculty Bibliography 2010s. 3427.