Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one

Abstract

The paper discusses nonlinear singular perturbations of delta type of the fractional Schrödinger equation $ı{\partial }_t\psi ={\left(-△\right)}^s\psi$, with $s\in (\frac{1}{2},1]$, in dimension one. Precisely, we investigate local and global well posedness (in a strong sense), conservations laws and existence of blow-up solutions and standing waves.

28 pages. Some minor revisions have been made with respect to the previous version