Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1899502 | Physica D: Nonlinear Phenomena | 2014 | 9 Pages |
Abstract
The critical nonlinear Schrödinger equation (NLS) possesses nearly self-similar ring profile solutions. We address the question of whether this profile is maintained all the way until the point of singularity. A perturbative analysis of the rescaled PDE and the resulting self-similar profile uncover slow dynamics that eventually drive the ring structure to the classical peak-shaped collapse instead. A numerical scheme capable of resolving self-similar behavior to high resolutions confirms our analysis. We also consider ring-type blowup arising either from azimuthally polarized solutions of a coupled NLS system or as vortex solutions of the usual NLS. In this case, the ring profile is maintained up to the time of singularity.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jordan Allen-Flowers, Karl B. Glasner,