Self-trapped pulsed beams with finite power in Kerr media excited by time-diffracting, space-time beams

We study the nonlinear propagation of space-time pulsed beams, also known as time-diffracting beams, a recently introduced class of diffraction-free spatiotemporal wave packets whose temporal-transversal structure is that of 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.