Abstract
We address the open problem of existence of singularities for the complex Ginzburg-Landau equation. Using a combination of rigorous results and numerical computations, we describe a countable family of self-similar singularities. Our analysis includes the supercritical nonlinear Schrödinger equation as a special case. We also consider the problem of stability of these singularities.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1215-1242 |
| Number of pages | 28 |
| Journal | Communications on Pure and Applied Mathematics |
| Volume | 54 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 2001 |