{
  "id": "1805.09637",
  "version": "v1",
  "published": "2018-05-24T12:41:52.000Z",
  "updated": "2018-05-24T12:41:52.000Z",
  "title": "The Construction of the mKdV $N$-soliton Solution by the Bäcklund Transformation",
  "authors": [
    "Masahito Hayashi",
    "Kazuyasu Shigemoto",
    "Takuya Tsukioka"
  ],
  "comment": "14 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We study group theoretical structures of the mKdV equation. The Schwarzian type mKdV equation has the global M\\\"{o}bius group symmetry. The Miura transformation makes a connection between the mKdV equation and the KdV equation. We find the special local M\\\"{o}bius transformation on the mKdV one-soliton solution which can be regarded as the commutative KdV B\\\"{a}cklund transformation can generate the mKdV $N$-soliton solution. In this algebraic construction to obtain multi-soliton solutions, we could observe the addition formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-24T12:41:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bäcklund transformation",
      "construction",
      "schwarzian type mkdv equation",
      "study group theoretical structures",
      "mkdv one-soliton solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}