Vortex filaments and ID cubic Schrödinger equations: Singularity formation

Research output: Contribution to journalArticlepeer-review

Colleges, School and Institutes

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.

Details

Original languageEnglish
Pages (from-to)457-474
Number of pages18
JournalCommunications in Applied Analysis
Volume15
Issue number2-4
Publication statusPublished - 1 Apr 2011