The dynamical problem of a spherically symmetric wave collapse is investigated in the framework of the nonlinear Schrödinger equation defined at the critical dimension. Collapsing solutions are shown to remain self-similar for spatial coordinates below a cutoff radius only, and to exhibit at larger distances a non-self-similar tail whose expression is explicitly computed. A rapid method used to study the time behavior and the stability of the contraction rate associated with these singular solutions is also derived.

• Received 11 May 1993

DOI:https://doi.org/10.1103/PhysRevE.48.R684