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Vortex solitons (dark solitons) are described in self-defocusing Kerr mediawhose phase line singularity is not parallel to the propagation direction, butis perpendicular or tilted almost arbitrary angles, depending on the mediumlinear dispersion. These solitons broaden the so-called spatiotemporal opticalvortices recently observed in experiments to the nonlinear realm, opening newperspectives in practical applications of optical vortices.

Spatiotemporal optical vortex solitons: Dark solitons with transverse and tilted phase line singularities