NON-SELF-SIMILAR COLLAPSING SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION AT THE CRITICAL DIMENSION

The dynamical problem of a spherically symmetric wave collapse is inve stigated in the framework of the nonlinear Schrodinger equation define d at the critical dimension. Collapsing solutions are shown to remain self-similar for spatial coordinates below a cutoff radius only, and t o exhibit at larger distances a non-self-similar tail whose expression is explicitly computed. A rapid method used to study the time behavio r and the stability of the contraction rate associated with these sing ular solutions is also derived.