{
  "id": "1408.4613",
  "version": "v1",
  "published": "2014-08-20T11:43:43.000Z",
  "updated": "2014-08-20T11:43:43.000Z",
  "title": "Bifurcations for a Coupled Schrödinger System with Multiple Components",
  "authors": [
    "Thomas Bartsch",
    "Rushun Tian",
    "Zhi-Qiang Wang"
  ],
  "comment": "16 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study local bifurcations of an indefinite elliptic system with multiple components: \\begin{equation*} \\left\\{\\begin{array}{ll} -\\Delta u_j + au_j = \\mu_ju_j^3+\\beta\\sum_{k\\ne j}u_k^2u_j, u_j>0\\ \\ \\hbox{in}\\ \\Omega, u_j=0 \\ \\ \\hbox{on}\\ \\partial\\Omega,\\ j=1,\\dots,n. \\end{array} \\right. \\end{equation*} Here $\\Omega\\subset{\\mathbb{R}}^N$ is a smooth and bounded domain, $n\\ge3$, $a<-\\Lambda_1$ where $\\Lambda_1$ is the principal eigenvalue of $(-\\Delta, H_0^1(\\Omega))$; $\\mu_j$ and $\\beta$ are real constants. Using the positive and non-degenerate solution of the scalar equation $-\\Delta\\omega-\\omega=-\\omega^3$, $\\omega\\in H_0^1(\\Omega)$, we construct a synchronized solution branch $\\mathcal{T}_\\omega$. Then we find a sequence of local bifurcations with respect to $\\mathcal{T}_\\omega$, and we find global bifurcation branches of partially synchronized solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-20T11:43:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B32",
      "35J50",
      "35J57",
      "35J61",
      "47J15",
      "58E07"
    ],
    "keywords": [
      "coupled schrödinger system",
      "multiple components",
      "global bifurcation branches",
      "indefinite elliptic system",
      "study local bifurcations"
    ],
    "publication": {
      "doi": "10.1007/s00033-015-0498-x",
      "journal": "Zeitschrift Angewandte Mathematik und Physik",
      "year": 2015,
      "month": "Oct",
      "volume": 66,
      "number": 5,
      "pages": 2109
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015ZaMP...66.2109B"
    }
  }
}