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The phase ``jumps'' for solitons interacting on a vortex filament, observedin experiments, have been unaccounted for since more than twenty years. Usingexplicit formulas describing the interaction of two solitons on a thin vortexfilament in the Localized Induction Approximation we show that an appropriatechoice of the parameters of the solitons leads to large phase shifts. Thisresult does not depend on the axial flow along the filament.Comment: 10 page

Why the Phase Shifts for Solitons on a Vortex Filament Are So Large: A Theoretical Explanation