{
  "id": "1405.3500",
  "version": "v2",
  "published": "2014-05-14T14:04:00.000Z",
  "updated": "2015-08-31T17:16:35.000Z",
  "title": "Initial value problems for integrable systems on a semi-strip",
  "authors": [
    "Alexander Sakhnovich"
  ],
  "comment": "In this paper, boundary conditions are recovered from the initial ones. The paper supplements in this respect our previous article arXiv:1403.8111, where initial conditions are recovered from the boundary conditions. Several explanations and references are added in the second version of the paper",
  "categories": [
    "math.AP",
    "math-ph",
    "math.CA",
    "math.MP",
    "math.SP",
    "nlin.SI"
  ],
  "abstract": "Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schroedinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonlinear Schroedinger equation.) Next, a special case of the nonlinear optics (N-wave) equation is considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-14T14:04:00.000Z",
      "abstract": "Two important cases, where solutions of integrable equations on a semi-strip are uniquely defined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schroedinger equation with quasi-analytic boundary conditions is dealt with. Next, a special case of the nonlinear optics (N-wave) equation is considered.",
      "comment": "In this paper, boundary conditions are recovered from the initial ones. The paper supplements in this respect our previous paper arXiv:1403.8111, where initial conditions are recovered from the boundary conditions",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-31T17:16:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35Q60",
      "34B20",
      "35A02"
    ],
    "keywords": [
      "initial value problems",
      "integrable systems",
      "semi-strip",
      "quasi-analytic boundary conditions",
      "defocusing nonlinear schroedinger equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.3500S"
    }
  }
}