{
  "id": "2409.01842",
  "version": "v2",
  "published": "2024-09-03T12:40:49.000Z",
  "updated": "2024-12-04T11:47:01.000Z",
  "title": "Stable standing waves for Nonlinear Schrödinger-Poisson system with a doping profile",
  "authors": [
    "Mathieu Colin",
    "Tatsuya Watanabe"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "This paper is devoted to the study of the nonlinear Schr\\\"odinger-Poisson system with a doping profile. We are interested in the existence of stable standing waves by considering the associated $L^2$-minimization problem. The presence of a doping profile causes a difficulty in the proof of the strict sub-additivity. A key ingredient is to establish the strict sub-additivity by adapting a scaling argument, which is inspired by \\cite{ZZou}. When the doping profile is a characteristic function supported on a bounded smooth domain, smallness of some geometric quantity related to the domain ensures the existence of stable standing waves.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-12-04T11:47:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35B35",
      "35Q55"
    ],
    "keywords": [
      "stable standing waves",
      "nonlinear schrödinger-poisson system",
      "doping profile",
      "strict sub-additivity",
      "minimization problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}