{
  "id": "1208.1570",
  "version": "v1",
  "published": "2012-08-08T03:33:22.000Z",
  "updated": "2012-08-08T03:33:22.000Z",
  "title": "Multi-component Wronskian solution to the Kadomtsev-Petviashvili equation",
  "authors": [
    "Tao Xu",
    "Fu-Wei Sun",
    "Yi Zhang",
    "Juan Li"
  ],
  "comment": "24 pages, 6 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is known that the Kadomtsev-Petviashvili (KP) equation can be decomposed into the first two members of the coupled Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy by the binary nonlinearization of Lax pairs. In this paper, we construct the N-th iterated Darboux transformation (DT) for the second- and third-order m-coupled AKNS systems. By using together the N-th iterated DT and Cramer's rule, we find that the KPII equation has the unreduced multi-component Wronskian solution and the KPI equation admits a reduced multi-component Wronskian solution. In particular, based on the unreduced and reduced two-component Wronskians, we obtain two families of fully-resonant line-soliton solutions which contain arbitrary numbers of asymptotic solitons as y->\\mp\\infty to the KPII equation, and the ordinary N-soliton solution to the KPI equation. In addition, we find that the KPI line solitons propagating in parallel can exhibit the bound state at the moment of collision.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-08T03:33:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kadomtsev-petviashvili equation",
      "kpii equation",
      "kpi line solitons",
      "third-order m-coupled akns systems",
      "unreduced multi-component wronskian solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1570X"
    }
  }
}