Vortex filament motion under the localized induction approximation in terms of Weierstrass elliptic functions

We study quasiperiodic solutions of the localized induction approximation in terms of the elliptic functions of Weierstrass. They describe the Kida-class motion of a thin vortex filament in an incompressible inviscid fluid. Our solution includes various filament shapes such as the vortex ring, the helicoidal filament, the plane sinusoidal filament, and the Hasimoto type-1 soliton filament.