Spatiotemporal instabilities in dispersive nonlinear media.

A spatiotemporal instability is shown to occur in a dispersive nonlinear optical medium whose refractive index varies linearly with the optical intensity (the Kerr medium). The physical origin of the spatiotemporal instability lies in the simultaneous presence of diffraction and dispersion in nonlinear media. For a self-focusing medium the instability can occur for both normal and anomalous dispersion