Exact Solution to Localized-Induction-Approximation Equation Modeling Smoke Ring Motion

J. Cieśliński, P.K.H. Gragert, A. Sym

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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.
Original languageUndefined
Pages (from-to)1507-1510
JournalPhysical review letters
Issue number13
Publication statusPublished - 1986


  • IR-61209

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