{
  "id": "math/0701786",
  "version": "v3",
  "published": "2007-01-26T21:22:40.000Z",
  "updated": "2007-08-01T21:59:29.000Z",
  "title": "Global Well-Posedness and Non-linear Stability of Periodic Traveling Waves for a Schrodinger-Benjamin-Ono System",
  "authors": [
    "Jaime Angulo",
    "Carlos Matheus",
    "Didier Pilod"
  ],
  "comment": "38 pages; typos corrected and global well-posedness theorem (in the continuous case) reworked to follow closely the arguments of Colliander, Holmes and Tzirakis",
  "categories": [
    "math.AP"
  ],
  "abstract": "The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schr\\\"odinger-Benjamin-Ono system) for \\emph{low-regularity} initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schr\\\"odinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called {\\it dnoidal}, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-08-01T21:59:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic traveling waves",
      "schrodinger-benjamin-ono system",
      "global well-posedness",
      "non-linear stability",
      "jacobian elliptic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1786A"
    }
  }
}