{
  "id": "math-ph/0503028",
  "version": "v2",
  "published": "2005-03-11T16:45:21.000Z",
  "updated": "2006-02-21T15:07:29.000Z",
  "title": "Solving bi-directional soliton equations in the KP hierarchy by gauge transformation",
  "authors": [
    "Jingsong He",
    "Yi Cheng",
    "Rudolf A. Roemer"
  ],
  "comment": "32 pages, 8 figures, high quality figures can be downloaded from http://eprints.csc.warwick.ac.uk/archive/00000103/",
  "journal": "JHEP 0603 (2006) 103",
  "doi": "10.1088/1126-6708/2006/03/103",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present a systematic way to construct solutions of the (n=5)-reduction of the BKP and CKP hierarchies from the general tau function of the KP hierarchy. We obtain the one-soliton, two-soliton, and periodic solution for the bi-directional Sawada-Kotera (bSK), the bi-directional Kaup-Kupershmidt (bKK) and also the bi-directional Satsuma-Hirota (bSH) equation. Different solutions such as left- and right-going solitons are classified according to the symmetries of the 5th roots of exp(i epsilon). Furthermore, we show that the soliton solutions of the n-reduction of the BKP and CKP hierarchies with n= 2 j +1, j=1, 2, 3, ..., can propagate along j directions in the 1+1 space-time domain. Each such direction corresponds to one symmetric distribution of the nth roots of exp(i epsilon). Based on this classification, we detail the existence of two-peak solitons of the n-reduction from the Grammian tau function of the sub-hierarchies BKP and CKP. If n is even, we again find two-peak solitons. Last, we obtain the \"stationary\" soliton for the higher-order KP hierarchy.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-21T15:07:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q51",
      "37K10",
      "82C23"
    ],
    "keywords": [
      "solving bi-directional soliton equations",
      "gauge transformation",
      "ckp hierarchies",
      "two-peak solitons",
      "grammian tau function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP",
      "journal": "Journal of High Energy Physics",
      "year": 2006,
      "month": "Apr",
      "volume": 2006,
      "number": 3,
      "pages": 103
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 704559,
      "adsabs": "2006JHEP...03..103H"
    }
  }
}