On the non-linear Schrödinger equation with a point interaction – Raffaele Scandone (Università degli Studi di Napoli Federico II)


Aula Seminari


In this talk I will discuss the Schrödinger operators with point interaction, which model the dynamics of a quantum particle interacting with a spatial defect. After introducing the adapted Sobolev spaces and the dispersive properties of the associated unitary evolution, I will consider the corresponding non-linear Schrödinger equation. Some recent results on the local and global well-posedness and the existence of standing waves solutions will be provided

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