Regime of wave-packet self-action in a medium with normal dispersion of the group velocity

Peculiar features of the self-action of non-one-dimensional wave packets described by the nonlinear Schrödinger equation with a hyperbolic spatial operator were studied analytically and numerically. It was shown that the self-action dynamics is determined by the consequence of the processes of transverse self-focusing filamentation and longitudinal splitting. Splitting scenarios were classified. It is shown that the strongest inhomogeneities are excited along “hyperbolas” in the self-similar collapse process.