Why the phase shifts for solitons on a vortex filament are so large?

Abstract

The phase ``jumps'' for solitons interacting on a vortex filament, observed in experiments, have been unaccounted for since more than twenty years. Using explicit formulas describing the interaction of two solitons on a thin vortex filament in the Localized Induction Approximation we show that an appropriate choice of the parameters of the solitons leads to large phase shifts. This result does not depend on the axial flow along the filament.