{
  "id": "1707.06225",
  "version": "v1",
  "published": "2017-07-18T11:37:46.000Z",
  "updated": "2017-07-18T11:37:46.000Z",
  "title": "Waves along fractal coastlines: From fractal arithmetic to wave equations",
  "authors": [
    "Marek Czachor"
  ],
  "comment": "First version of the paper was submitted to arXiv on 9 Jul 2017",
  "categories": [
    "math.DS",
    "nlin.CD",
    "nlin.PS"
  ],
  "abstract": "Beginning with addition and multiplication which are intrinsic to a Koch-type curve, I formulate and solve a wave equation that describes wave propagation along a fractal coastline. As opposed to the examples known from the literature I do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-18T11:37:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wave equation",
      "fractal coastline",
      "fractal arithmetic",
      "wave propagation",
      "first example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}