• Corpus ID: 216036036

# Fractional Schr\"{o}dinger Equations with potentials of higher-order singularities

@article{Altybay2020FractionalSE,
title={Fractional Schr\"\{o\}dinger Equations with potentials of higher-order singularities},
author={Arshyn Altybay and Michael Ruzhansky and Mohammed Elamine Sebih and Niyaz Tokmagambetov},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Published 21 April 2020
• Mathematics
• arXiv: Analysis of PDEs
In this paper, we consider the space-fractional Schrodinger equation with a singular potential. We show that it has a so-called very weak solutions. The uniqueness and consistency results are proved in an appropriate sense. Numerical simulations are done, and a particle accumulating effect is observed. From the mathematical point of view, a "splitting of the strong singularity" phenomena is observed.
2 Citations

## Figures from this paper

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• Mathematics
ArXiv
• 2020
A tsunami wave equation with singular coefficients is considered and it is proved that it has a very weak solution, and the uniqueness results and consistency theorem of the veryweak solution with the classical one in some appropriate sense are shown.

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