<I>N</I>-Solitons on a Curved Vortex Filament

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  • N-Solitons on a Curved Vortex Filament

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The motion of a thin vortex filament in an incompressible inviscid fluid is investigated theoretically, based on the localized induction equation. The N-soliton solution is given explicitly, using the bilinear equations obtained by Hirota. A detailed examination of the solution shows that two solitons with large lateral excursion suffer backward phase-shifts during a head-on collision. The present solution also generates the N-soliton solution of the classical 1-dim. continuous Heisenberg ferromagnet equation.

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