{
  "id": "2208.11240",
  "version": "v1",
  "published": "2022-08-24T00:21:26.000Z",
  "updated": "2022-08-24T00:21:26.000Z",
  "title": "On the NLS approximation for the nonlinear Klein-Gordon equation",
  "authors": [
    "Seokchang Hong",
    "Younghun Hong"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class solutions which are formally asymptotically in $L^2(\\mathbb{R})$. A precise rate of convergence is also obtained assuming more regularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-24T00:21:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear klein-gordon equation",
      "one-dimensional cubic klein-gordon equation",
      "low regularity nls approximation",
      "fourier analysis methods",
      "energy class solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}