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arXiv · 1805.06952

Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one

Raffaele Carlone·Domenico Finco·Lorenzo Tentarelli
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Abstract

The paper discusses nonlinear singular perturbations of delta type of the fractional Schrödinger equation $\imath\partial_tψ=\left(-\triangle\right)^sψ$, 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.

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Raffaele Carlone, Domenico Finco, Lorenzo Tentarelli. 2019-03-25. Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one. https://doi.org/10.1088/1361-6544%2Fab1273

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