{
  "id": "2402.16222",
  "version": "v2",
  "published": "2024-02-25T23:49:39.000Z",
  "updated": "2024-03-02T15:52:56.000Z",
  "title": "Orbital Stability of Soliton for the Derivative Nonlinear Schrödinger Equation in the $L^2$ Space",
  "authors": [
    "Yiling Yang",
    "Engui Fan",
    "Yue Liu"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we establish the orbital stability of the 1-soliton solution for the derivative nonlinear Schr\\\"odinger equation under perturbations in $L^2(\\mathbb{R})$. We demonstrate this stability by utilizing the B\\\"acklund transformation associated with the Lax pair and by applying the first conservation quantity in $L^2(\\mathbb{R}).$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-03-02T15:52:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q51",
      "35Q15",
      "37K15",
      "35Q35"
    ],
    "keywords": [
      "derivative nonlinear schrödinger equation",
      "orbital stability",
      "first conservation quantity",
      "lax pair",
      "transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}