Now showing items 1-6 of 6

    • Dispersion for the Schrödinger equation on networks 

      Banica, V.; Ignat, L.I. (2011-12-31)
      In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schrödinger ...
    • Evolution of Polygonal Lines by the Binormal Flow 

      Banica, V.; Vega, L.Autoridad BCAM (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 

      Banica, V.; Vega, L.Autoridad BCAM (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 ...
    • Riemann's non-differentiable function and the binormal curvature flow 

      Banica, V.; Vega, L.Autoridad BCAM (2020-07-14)
      We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object ...
    • Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$ 

      Banica, V.; Vega, L.Autoridad BCAM (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 

      Banica, V.; Vega, L.Autoridad BCAM (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 ...