{
  "id": "0905.3834",
  "version": "v1",
  "published": "2009-05-23T17:01:54.000Z",
  "updated": "2009-05-23T17:01:54.000Z",
  "title": "Self-similar Solutions of the Cubic Wave Equation",
  "authors": [
    "P. Bizoń",
    "P. Breitenlohner",
    "D. Maison",
    "A. Wasserman"
  ],
  "comment": "14 pages, 1 figure",
  "journal": "Nonlinearity 23:225-236,2010",
  "doi": "10.1088/0951-7715/23/2/002",
  "categories": [
    "math.AP",
    "gr-qc"
  ],
  "abstract": "We prove that the focusing cubic wave equation in three spatial dimensions has a countable family of self-similar solutions which are smooth inside the past light cone of the singularity. These solutions are labeled by an integer index $n$ which counts the number of oscillations of the solution. The linearized operator around the $n$-th solution is shown to have $n+1$ negative eigenvalues (one of which corresponds to the gauge mode) which implies that all $n>0$ solutions are unstable. It is also shown that all $n>0$ solutions have a singularity outside the past light cone which casts doubt on whether these solutions may participate in the Cauchy evolution, even for non-generic initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-23T17:01:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-similar solutions",
      "past light cone",
      "focusing cubic wave equation",
      "non-generic initial data",
      "spatial dimensions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2010,
      "month": "Feb",
      "volume": 23,
      "number": 2,
      "pages": 225
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 854347,
      "adsabs": "2010Nonli..23..225B"
    }
  }
}