1-D cubic NLS with several Dirac masses as initial data and consequences

Banica, Valeria

Séminaire Laurent Schwartz — EDP et applications (2017-2018), Exposé no. 3, 9 p.

In this proceedings article we present a result on the 1-D cubic nonlinear Schrödinger equation with a sum of Dirac masses as initial data. We shall give a sketch of the proof. By using this result we show how to construct the evolution in time of a polygonal line through the binormal flow. This equation is a geometric flow for curves in ${ℝ}^3$ and it is used as a model for the evolution of a vortex filament in fluid mechanics. These results were obtained in collaboration with Luis Vega in [4].

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