{
  "id": "0906.0351",
  "version": "v1",
  "published": "2009-06-01T20:25:33.000Z",
  "updated": "2009-06-01T20:25:33.000Z",
  "title": "Dispersive estimates using scattering theory for matrix Hamiltonian equations",
  "authors": [
    "Jeremy Marzuola"
  ],
  "comment": "48 pages, 3 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We develop the techniques of \\cite{KS1} and \\cite{ES1} in order to derive dispersive estimates for a matrix Hamiltonian equation defined by linearizing about a minimal mass soliton solution of a saturated, focussing nonlinear Schr\\\"odinger equation {c} i u_t + \\Delta u + \\beta (|u|^2) u = 0 u(0,x) = u_0 (x), in $\\reals^3$. These results have been seen before, though we present a new approach using scattering theory techniques. In further works, we will numerically and analytically study the existence of a minimal mass soliton, as well as the spectral assumptions made in the analysis presented here.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-01T20:25:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "35P10"
    ],
    "keywords": [
      "dispersive estimates",
      "minimal mass soliton solution",
      "matrix hamiltonian equation",
      "scattering theory techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.0351M"
    }
  }
}