1-d Cubic NLS with several Dirac deltas as initial condition: Talbot effect and Intermittency

PDE Seminar
Tuesday, November 21, 2017 - 15:00
1 hour (actually 50 minutes)
Skiles 006
University of the Basque Country UPV/EHU
The aim of talk is threefold. First, we solve the cubic nonlinear Schr\"odinger equation on the real line with initial data a sum of Dirac deltas. Secondly, we show a Talbot effect for the same equation. Finally, we prove an intermittency phenomena for a class of singular solutions of the binormal flow, that is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. If time permits some questions concerning the transfer of energy and momentum will be also considered.