Self-focusing dynamics of nonlinear waves in media with parabolic-type inhomogeneities

The possibility of accelerating the self-focusing dynamics of light beams in nonlinear and dispersive media with either a constant or a weakly oscillating parabolic density profile is investigated. It is shown that the self-compression of wave packets, that freely self-focus in homogeneous media, can be enhanced by the action of appropriate parabolic inhomogeneities, whose lensing influence shortens the focal time of the wave. A similar property also occurs when the scalar envelope of a nonlinear waveform interacts with a uniform external magnetic field. The motion of light beamlets, originating from the filamentation instability of an incident beam, is analytically described for inhomogeneous media with focusing and defocusing density profiles.