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

Non-analytic Vortex Core and a Nonlinear Vortex Flow in Bosonic Superfluids