Induced superspike in an enhanced induced-phase-modulation two-dimensional nonlinear medium

I show that a probe pulse that is copropagating in an enhanced induced-phase-modulation nonlinear two-dimensional medium in the presence of a pump may be transformed into an induced superspike in time and space. The conditions of this induced collapse are that the ratio of the probe and pump initial transverse dimension to the duration be equal to 1/[beta((2))k(probe)]((1/2)), that their group velocities be equal, that the pump energy be larger than a waveguiding critical value, and that the probe central frequency be in the group-velocity dispersion anomalous region.