We present and discuss a three-parameter class of exact solutions to the localized-induction-approximation equations. These are one-soliton excitations (B\"acklund 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.
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Cieśliński et al. (1986) studied this question.
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