{
  "id": "1612.08548",
  "version": "v1",
  "published": "2016-12-27T09:26:33.000Z",
  "updated": "2016-12-27T09:26:33.000Z",
  "title": "Similarity solutions of Fokker-Planck equation with time-dependent coefficients and fixed/moving boundaries",
  "authors": [
    "C. -L. Ho"
  ],
  "comment": "6 pages, 2 figures. Proceedings of the Conference in Honor of the 90th Birthday of Freeman Dyson, 2013/08/26-29, Nanyang Technological University, Singapore, World Scientific Publishing, 2014. (Based on talks given at the Dyson90 conference, and at \"12th Asia Pacific Physics Conference (APPC12), 2013/0/13-19, Makuhari, Japan\"). See arXiv:1403.3915 for extension of the work",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.AP",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulting ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker-Planck equations are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-27T09:26:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fokker-planck equation",
      "similarity solutions",
      "time-dependent coefficients",
      "fixed/moving boundaries",
      "probability current density vanishes"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}