The effects of normal dispersion on collapse events

It is shown analytically that positive or normal dispersion arrests at least the initial stage of the critical self-similar collapse events associated with the nonlinear Schrödinger equation. This is done by pertubing a wave packet that undergoes critical self similar collapse in d dimensions by adding weak positive dispersion in one additional direction. Singular perturbation analysis then yields a closed set of simple equations for the parameters of the collapsing mode from which it is clear that in the absence of normal dispersion the self similar collapse will continue while, in its presence, the collapse attractor disappears. Direct numerical integrations are in excellent agreement with the predictions of the simple reduced equations.