Abstract
A perturbation analysis with respect to the space dimension is used to construct singular solutions of the two-dimensional Schrödinger equation with cubic nonlinearity. These solutions blow up at a rate {ln ln[(-t]/(-t), 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.
- Received 7 March 1988
DOI:https://doi.org/10.1103/PhysRevA.38.3837
©1988 American Physical Society