  The dynamics of 3D Airy-vortex wave packets is studied under the action of
strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of
the main wave packets with the topological charges were demonstrated. Due to
the conservation of the total angular momentum, charges of the emitted waves
are equal to those carried by the parental light structure. The rapid collapse
imposes a severe limitation on the propagation of multidimensional waves in
Kerr media. However, the structure of the Airy beam carrier allows the coupling
of light from the leading, most intense peak into neighboring peaks and
consequently strongly postpones the collapse. The dependence of the critical
input amplitude for the appearance of a fast collapse on the beam width is
studied for wave packets with zero and non-zero topological charges. Wave
packets carrying angular momentum are found to be much more resistant to the
rapid collapse, especially those having small width.
