Dynamics of short-pulse splitting in dispersive nonlinear media

We develop a method to precisely propagate short optical pulses through dispersive media with a cubic self-focusing nonlinear polarization. We show that above the critical cw self-focusing power, onset of pulse splitting into pulselets separated in time occurs, and for a certain regime of parameters a cyclic series of pulse splitting (into pulselets separated in time) and pulse recombination occurs for diffraction length smaller than dispersion length. At higher power, another threshold for noncyclic temporal and spatial pulse splitting is manifest. The physics of these phenomena are described and delineated.