Evolution of light bullets propagating in saturable Kerr-like media with higher order effect

In the paper, propagation of spatio-temporal pulses (light bullets) in inhomogeneous, Kerr-like nonlinear medium is considered. For ultra-short bullets the higher-order nonlinear effects - self frequency shift and nonlinear dispersion together with saturation of nonlinear susceptibility are taken into account. The equations describing evolution of temporal and spatial width of the bullet parameters are derived. The stationary solutions of these equations are found analytically. Small oscillations around the stationary bullet's widths are considered and frequency oscillations are obtained. The regime of stable oscillations is discussed.