  We analyze the disorder limited motion of quantum vortices in a
two-dimensional bosonic superfluid with a large healing length. It is shown
that the excitations of low-energy degrees of freedom associated with the
non-analytic reconstruction of the vortex core [Ann. Phys. {\bf 346}, 195
(2014)] determine strong non-linear effects in the vortex transport at
velocities much smaller than Landau's critical velocity. Experiments are
suggested to verify our predictions.
