# 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} }

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

Tsunami propagation for singular topographies

- MathematicsArXiv
- 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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