Abstract
In this paper we will give an overview on some recent results and work in progress on self-similar solutions of the Localized Induction Approximation (LIA) leading to a phenomenon of singularity formation in finite time. A special emphasis will be drawn to the connection of this geometrical flow with certain nonlinear cubic Schrödinger equations in one space dimension through the so-called Hasimoto transformation.
| Original language | English |
|---|---|
| Pages (from-to) | 457-474 |
| Number of pages | 18 |
| Journal | Communications in Applied Analysis |
| Volume | 15 |
| Issue number | 2-4 |
| Publication status | Published - 1 Apr 2011 |
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics