  We study the nonlinear propagation of diffraction-free, space-time wave
packets, also called time-diffracting beams because their spatiotemporal
structure reproduces diffraction in time. We report on the spontaneous
formation of propagation-invariant, spatiotemporally compressed pulsed beams
carrying finite power from exciting time-diffracting Gaussian beams in media
with cubic Kerr nonlinearity at powers below the critical power for collapse,
and also with other collapse-arresting nonlinearities above the critical power.
Their attraction property makes the experimental observation of the
self-trapped pulsed beams in cubic Kerr media feasible. The structure in the
temporal and transversal dimensions of the self-trapped wave packets is shown
to be the same as the structure in the axial and transversal dimensions of the
self-focusing and (arrested) collapse of monochromatic Gaussian beams.
