{
  "id": "math/0506089",
  "version": "v2",
  "published": "2005-06-05T21:37:33.000Z",
  "updated": "2005-07-06T15:11:08.000Z",
  "title": "Quasi-periodic solutions of the equation v_{tt}-v_{xx}+v^3=f(v)",
  "authors": [
    "Pietro Baldi"
  ],
  "comment": "20 pages. Corrected some misprints, added a reference, moved Proposition and Lemma 1 from Section 2 to the Appendix",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider 1D completely resonant nonlinear wave equations of the type v_{tt}-v_{xx}=-v^3+O(v^4) with spatial periodic boundary conditions. We prove the existence of a new type of quasi-periodic small amplitude solutions with two frequencies, for more general nonlinearities. These solutions turn out to be, at the first order, the superposition of a traveling wave and a modulation of long period, depending only on time.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-07-06T15:11:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35B15",
      "37K50"
    ],
    "keywords": [
      "quasi-periodic solutions",
      "spatial periodic boundary conditions",
      "quasi-periodic small amplitude solutions",
      "resonant nonlinear wave equations",
      "long period"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6089B"
    }
  }
}