Key points are not available for this paper at this time.
A perturbation analysis with respect to the space dimension is used to construct singular solutions of the two-dimensional Schr\"odinger equation with cubic nonlinearity. These solutions blow up at a rate ln ln ({t^*-t) ^-1/ (t^*-t) }^1/2, in contrast to the behavior in three dimensions where there is no logarithmic correction. The form of such solutions is supported by the results of high-resolution numerical simulations.
Landman et al. (Sat,) studied this question.