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

J. Cieśliński; P.K.H. Gragert; A. Sym

doi:10.1103/PhysRevLett.57.1507

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

J. Cieśliński, P.K.H. Gragert, A. Sym

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Abstract

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 language	English
Pages (from-to)	1507-1510
Journal	Physical review letters
Volume	57
Issue number	13
DOIs	https://doi.org/10.1103/PhysRevLett.57.1507
Publication status	Published - 1986

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IR-61209

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title = "Exact Solution to Localized-Induction-Approximation Equation Modeling Smoke Ring Motion",

abstract = "We present and discuss a three-parameter class of exact solutions to the localized-induction-approximation equations. These are one-soliton excitations (B{\"a}cklund 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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year = "1986",

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T1 - Exact Solution to Localized-Induction-Approximation Equation Modeling Smoke Ring Motion

AU - Cieśliński, J.

AU - Gragert, P.K.H.

AU - Sym, A.

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

KW - IR-61209

U2 - 10.1103/PhysRevLett.57.1507

DO - 10.1103/PhysRevLett.57.1507

M3 - Article

SN - 0031-9007

VL - 57

SP - 1507

EP - 1510

JO - Physical review letters

JF - Physical review letters

IS - 13

ER -

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

Abstract

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