Now showing items 1-4 of 4

• #### Evolution of Polygonal Lines by the Binormal Flow ﻿

(2020-02-05)
The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ...
• #### On the energy of critical solutions of the binormal flow ﻿

(2019-07-20)
The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen- berg model in ferromagnetism, and the 1-D cubic Schr ...
• #### Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$ ﻿

(2017-02-02)
In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac-$\delta$ function and some other related equations. We first recall that although the problem for this type of ...
• #### The initial value problem for the binormal flow with rough data ﻿

(2015-12-31)
In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ...