{
  "id": "0909.3141",
  "version": "v3",
  "published": "2009-09-17T02:10:03.000Z",
  "updated": "2010-04-10T15:29:43.000Z",
  "title": "Solutions of the Nonlinear Schrodinger Equation with Prescribed Asymptotics at Infinity",
  "authors": [
    "John B. Gonzalez"
  ],
  "comment": "41 pages double spaced, accepted, added a few references, made some typographical changes, rewrote lemma A.1 part 6.",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove local existence and uniqueness of solutions for the one-dimensional nonlinear Schr\\\"odinger (NLS) equations $iu_t + u_{xx} \\pm |u|^2 u = 0$ in classes of smooth functions that admit an asymptotic expansion at infinity in decreasing powers of $x$. We show that an asymptotic solution differs from a genuine solution by a Schwartz class function which solves a generalized version of the NLS equation. The latter equation is solved by discretization methods. The proofs closely follow previous work done by the author and others on the Korteweg-De Vries (KdV) equation and the modified KdV equations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-04-10T15:29:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A01",
      "35A02",
      "35C20",
      "65M06"
    ],
    "keywords": [
      "nonlinear schrodinger equation",
      "prescribed asymptotics",
      "schwartz class function",
      "asymptotic solution differs",
      "genuine solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.3141G"
    }
  }
}