{
  "id": "2004.10182",
  "version": "v1",
  "published": "2020-04-21T17:46:25.000Z",
  "updated": "2020-04-21T17:46:25.000Z",
  "title": "Fractional Schrödinger Equations with potentials of higher-order singularities",
  "authors": [
    "Arshyn Altybay",
    "Michael Ruzhansky",
    "Mohammed Elamine Sebih",
    "Niyaz Tokmagambetov"
  ],
  "comment": "14 pages; 17 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the space-fractional Schr\\\"{o}dinger 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-21T17:46:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A21",
      "35D99",
      "35R11"
    ],
    "keywords": [
      "fractional schrödinger equations",
      "higher-order singularities",
      "particle accumulating effect",
      "singular potential",
      "strong singularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}