{
  "id": "1705.04206",
  "version": "v1",
  "published": "2017-05-10T12:36:06.000Z",
  "updated": "2017-05-10T12:36:06.000Z",
  "title": "Nonlinear stability of Gardner breathers",
  "authors": [
    "Miguel A. Alejo"
  ],
  "comment": "30 pages, 2 figs. Submitted. arXiv admin note: substantial text overlap with arXiv:1206.3157",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are globally stable in a \\emph{natural} $H^2$ topology. Our proof presentsa systematic and simple account that put in evidence that the Gardner breather solutions satisfy a suitable variational elliptic equation, which also implies that the stability problem reduces in some sense to $(i)$ the study of the spectrum of explicit linear systems (\\emph{spectral stability}), and $(ii)$ the understanding of how degenerated directions can be controlled using low regularity conservation laws.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-10T12:36:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q51",
      "35Q53",
      "37K10",
      "37K40"
    ],
    "keywords": [
      "nonlinear stability",
      "low regularity conservation laws",
      "gardner breather solutions satisfy",
      "explicit linear systems",
      "stability problem reduces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}