Vortex filaments and ID cubic Schrödinger equations: Singularity formation
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Colleges, School and Institutes
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.
|Number of pages||18|
|Journal||Communications in Applied Analysis|
|Publication status||Published - 1 Apr 2011|