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In recognition of the highly non-trivial task of computation of the inverseHasimoto transformation mapping the intrinsic geometric parameter space ontothe extrinsic vortex filament coordinate space a reformulation of the DaRios-Betchov equations in the latter space is given. The nonlinear localizedvortex filament structure solution given by the present formulation is indetailed agreement with the Betchov-Hasimoto solution in the small-amplitudelimit and is also in qualitative agreement with laboratory experimentobservations of helical-twist solitary waves propagating on concentratedvortices in rotating fluids. The present formulation also provides for adiscernible effect of the slipping motion of a vortex filament on the vortexevolution.

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Motion of a Vortex Filament in the Local Induction Approximation:  Reformulation of the Da Rios-Betchov Equations in the Extrinsic Filament  Coordinate Space