{
  "id": "1912.11459",
  "version": "v1",
  "published": "2019-12-24T18:26:44.000Z",
  "updated": "2019-12-24T18:26:44.000Z",
  "title": "On the nonlinear Dirac equation on noncompact metric graphs",
  "authors": [
    "William Borrelli",
    "Raffaele Carlone",
    "Lorenzo Tentarelli"
  ],
  "comment": "29 pages, 4 figures. Keywords: nonlinear Dirac equation, metric graphs, local well-posedness, bound states, implicit function theorem, bifurcation, perturbation method, nonrelativistic limit",
  "categories": [
    "math.AP",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "The paper discusses the Nonlinear Dirac Equation with Kerr-type nonlinearity (i.e., $\\psi^{p-2}\\psi$) on noncompact metric graphs with a finite number of edges, in the case of Kirchhoff-type vertex conditions. Precisely, we prove local well-posedness for the associated Cauchy problem in the operator domain and, for infinite $N$-star graphs, the existence of standing waves bifurcating from the trivial solution at $\\omega=mc^2$, for any $p>2$. In the Appendix we also discuss the nonrelativistic limit of the Dirac-Kirchhoff operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-24T18:26:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R02",
      "35Q41",
      "81Q35",
      "47J07",
      "58E07",
      "47A10"
    ],
    "keywords": [
      "nonlinear dirac equation",
      "noncompact metric graphs",
      "kirchhoff-type vertex conditions",
      "paper discusses",
      "trivial solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}