Large transverse shifts appearing upon passage of vortices through oblique dark solitons

We show that when a single vortex convected by a flowing background collides with an oblique dark soliton in defocusing Kerr-type medium, it passes through the oblique soliton, but this process is accompanied by a considerable vertical shift of the vortex that grows with decrease of the inclination angle of the dark soliton with respect to the direction of the flow and decreases with increase of the flow (or collision) velocity. In the parameter range where the interaction with a vortex does not lead to drastic deformations of the shape of the oblique dark soliton, this shift can be estimated analytically under the assumption that vortex soliton moves along the "stream lines" that exhibit vertical shift in the vicinity of oblique dark soliton. Similar effect was observed upon collision of dark solitons with moving vortex dipoles or rotating pairs of vortices with equal topological charges.