{
  "id": "1404.7581",
  "version": "v2",
  "published": "2014-04-30T03:04:31.000Z",
  "updated": "2014-10-12T04:03:51.000Z",
  "title": "Global bounds for the cubic nonlinear Schrödinger equation (NLS) in one space dimension",
  "authors": [
    "Mihaela Ifrim",
    "Daniel Tataru"
  ],
  "comment": "15 pages. We fixed the proof of Lemma 2.4",
  "categories": [
    "math.AP"
  ],
  "abstract": "This article is concerned with the small data problem for the cubic nonlinear Schr\\\"odinger equation (NLS) in one space dimension, and short range modifications of it. We provide a new, simpler approach in order to prove that global solutions exist for data which is small in $H^{0,1}$. In the same setting we also discuss the related problems of obtaining a modified scattering expansion for the solution, as well as asymptotic completeness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-30T03:04:31.000Z",
      "comment": "15 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-12T04:03:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "cubic nonlinear schrödinger equation",
      "space dimension",
      "global bounds",
      "small data problem",
      "short range modifications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.7581I"
    }
  }
}