  A vortex filament immersed in a non-ideal fluid, thanks to viscous diffusion,
experiences a slipping motion with respect to the fluid. In recognition of
this, in this paper, the effect of this slipping motion on the Hasimoto soliton
propagating on a vortex filament is investigated, and an exact solution is
given to describe this process. A strong slipping motion is shown to prevent
the existence of the Hasimoto soliton. The critical slipping speed (above which
the Hasimoto soliton fails to exist) is shown to be equal to the torsion.
