{
  "id": "2403.16648",
  "version": "v2",
  "published": "2024-03-25T11:35:52.000Z",
  "updated": "2024-04-11T11:59:52.000Z",
  "title": "On the Korteweg-de Vries limit for the Boussinesq equation",
  "authors": [
    "Younghun Hong",
    "Changhun Yang"
  ],
  "comment": "17 pages, V1:Minor typos are corrected",
  "categories": [
    "math.AP"
  ],
  "abstract": "The Korteweg-de Vries (KdV) equation is known as a universal equation describing various long waves in dispersive systems. In this article, we prove that in a certain scaling regime, a large class of rough solutions to the Boussinesq equation are approximated by the sums of two counter-propagating waves solving the KdV equations. It extends the earlier result by \\cite{Schneider1998} to slightly more regular than $L^2$-solutions. Our proof is based on robust Fourier analysis methods developed for the low regularity theory of nonlinear dispersive equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-04-11T11:59:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "76B15"
    ],
    "keywords": [
      "korteweg-de vries limit",
      "boussinesq equation",
      "robust fourier analysis methods",
      "low regularity theory",
      "kdv equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}