{
  "id": "1410.6873",
  "version": "v1",
  "published": "2014-10-25T02:52:25.000Z",
  "updated": "2014-10-25T02:52:25.000Z",
  "title": "Asymptotic Stability for KdV Solitons in Weighted $H^s$ Spaces",
  "authors": [
    "Brian Pigott",
    "Sarah Raynor"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentially-weighted norms. Using a combination of the $I$-method and spectral analysis following Pego and Weinstein, we are able to show that, in the exponentially weighted space, the perturbation of a soliton decays exponentially for arbitrarily long times. The finite time restriction is due to a lack of global control of the unweighted perturbation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-25T02:52:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kdv solitons",
      "asymptotic stability",
      "finite time restriction",
      "kdv equation",
      "energy space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.6873P"
    }
  }
}