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., 346 (2014) 195) 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.
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