{
  "id": "2111.15136",
  "version": "v2",
  "published": "2021-11-30T05:31:03.000Z",
  "updated": "2023-01-06T02:56:45.000Z",
  "title": "Orbital stability of two-component peakons",
  "authors": [
    "Cheng He",
    "Xiaochuan Liu",
    "Changzheng Qu"
  ],
  "comment": "Accepted for publication",
  "journal": "SCIENCE CHINA Mathematics in 2023",
  "categories": [
    "math.AP",
    "nlin.SI"
  ],
  "abstract": "We prove that the two-component peakon solutions are orbitally stable in the energy space. The system concerned here is a two-component Novikov system, which is an integrable multicomponent extension of the integrable Novikov equation. We improve the method for the scalar peakons to the two-component case with genuine nonlinear interactions by establishing optimal inequalities for the conserved quantities involving the coupled structures. Moreover, we also establish the orbital stability for the train-profiles of these two-component peakons by using the refined analysis based on monotonicity of the local energy and an induction method.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-01-06T02:56:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orbital stability",
      "two-component peakon solutions",
      "two-component novikov system",
      "genuine nonlinear interactions",
      "energy space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}