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arXiv · 1805.06952

Nonlinear singular perturbations of the fractional Schr\"odinger 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 Schr\"odinger equation $\imath\partial_t\psi=\left(-\triangle\right)^s\psi$, 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.

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Raffaele Carlone, Domenico Finco, Lorenzo Tentarelli. 2018-05-17. Nonlinear singular perturbations of the fractional Schr\"odinger equation in dimension one. https://doi.org/10.1088/1361-6544/ab1273

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