Abstract:
In this talk, we shall prove the existence of dispersive blow-up for the Schrödinger-Korteweg-de Vries system. Roughly, dispersive blow-up has being called to the development of point singularities due to the focussing of short or long waves. In mathematical terms, we show that the existence of this kind of singularities is provided by the linear dispersive solution by proving that the Duhamel term is smoother. This result is the first one regarding systems of nonlinear dispersive equations. To obtain our results we use, in addition to smoothing properties, persistence properties for solutions of the IVP in fractional weighted Sobolev spaces which we establish here.