{
  "id": "2407.19141",
  "version": "v1",
  "published": "2024-07-27T01:20:05.000Z",
  "updated": "2024-07-27T01:20:05.000Z",
  "title": "Asymptotic profile of least energy solutions to the nonlinear Schrödinger-Bopp-Podolsky system",
  "authors": [
    "Gustavo de Paula Ramos"
  ],
  "comment": "12 pages, comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "Consider the following nonlinear Schr\\\"odinger--Bopp--Podolsky system in $\\mathbb{R}^3$: \\[ \\begin{cases} - \\Delta v + v + \\phi v = v |v|^{p - 2}; \\\\ \\beta^2 \\Delta^2 \\phi - \\Delta \\phi = 4 \\pi v^2, \\end{cases} \\] where $\\beta > 0$ and $3 < p < 6$, the unknowns being $v$, $\\phi \\colon \\mathbb{R}^3 \\to \\mathbb{R}$. We prove that, as $\\beta \\to 0$ and up to translations and subsequences, least energy solutions to this system converge to a least energy solution to the following nonlinear Schr\\\"odinger--Poisson system in $\\mathbb{R}^3$: \\[ \\begin{cases} - \\Delta v + v + \\phi v = v |v|^{p - 2}; \\\\ - \\Delta \\phi = 4 \\pi v^2. \\end{cases} \\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-27T01:20:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "energy solution",
      "nonlinear schrödinger-bopp-podolsky system",
      "asymptotic profile",
      "system converge"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}