{
  "id": "2311.09949",
  "version": "v1",
  "published": "2023-11-16T15:05:25.000Z",
  "updated": "2023-11-16T15:05:25.000Z",
  "title": "2-peaks cluster solutions to the nonlinear Schrödinger-Bopp-Podolsky system",
  "authors": [
    "Gustavo de Paula Ramos"
  ],
  "comment": "21 pages; comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "Suppose that $z_0$ is a local strict minimum point of $V \\colon \\mathbb{R}^3 \\to ]0, \\infty[$ and $V$ is adequately flat around $z_0$. We employ Lyapunov-Schmidt reduction to prove that if $\\epsilon > 0$ is sufficiently small, then the nonlinear Schr\\\"odinger-Bopp-Podolsky system \\[ \\begin{cases} -\\epsilon^2 \\Delta u + (V + \\phi) u = u |u|^{p-1}; \\newline \\Delta^2 \\phi - \\Delta \\phi = 4 \\pi u^2 \\end{cases} ~\\text{in}~\\mathbb{R}^3 \\] has a $2$-peaks solution and the corresponding peaks converge to $z_0$ as $\\epsilon \\to 0^+$, where $1 < p < 5$ and our unknowns are $u, \\phi\\colon\\mathbb{R}^3\\to\\mathbb{R}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-16T15:05:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear schrödinger-bopp-podolsky system",
      "cluster solutions",
      "local strict minimum point",
      "employ lyapunov-schmidt reduction",
      "peaks solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}