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.

arXiv comment28 pages. Some minor revisions have been made with respect to the previous version

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Cited by in corpus (8)

• Ground states for the planar NLSE with a point defect as minimizers of the constrained energy
• Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect
• Blow-up for the pointwise NLS in dimension two: absence of critical power
• Stability of the standing waves of the concentrated NLSE in dimension two
• A general review on the NLS equation with point-concentrated nonlinearity
• Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one
• Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity
• Normalized solutions of one-dimensional defocusing NLS equations with nonlinear point interactions