We present and discuss a three-parameter class of exact solutions to the localized-induction-approximation equations. These are one-soliton excitations (Bäcklund transforms) of the circular vortex motion. The corresponding generic vortex filament (of infinite or finite length) remains in the interior of the sphere (or torus) moving with a constant velocity. The above solutions generate a new class of exact solutions to the classical one-dimensional continuous Heisenberg ferromagnet model.
Cieśliński, J., Gragert, P. K. H., & Sym, A. (1986). Exact Solution to Localized-Induction-Approximation Equation Modeling Smoke Ring Motion. Physical review letters, 57(13), 1507-1510. https://doi.org/10.1103/PhysRevLett.57.1507