{
  "id": "1006.0458",
  "version": "v2",
  "published": "2010-06-02T18:01:41.000Z",
  "updated": "2010-10-05T14:39:02.000Z",
  "title": "The Kadomtsev-Petviashvili II Equation on the Half-Plane",
  "authors": [
    "D. Mantzavinos",
    "A. S. Fokas"
  ],
  "comment": "49 pages, 9 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The KPII equation is an integrable nonlinear PDE in 2+1 dimensions (two spatial and one temporal), which arises in several physical circumstances, including fluid mechanics where it describes waves in shallow water. It provides a multidimensional generalisation of the renowned KdV equation. In this work, we employ a novel approach recently introduced by one of the authors in connection with the Davey-Stewartson equation \\cite{FDS2009}, in order to analyse the initial-boundary value problem for the KPII equation formulated on the half-plane. The analysis makes crucial use of the so-called d-bar formalism, as well as of the so-called global relation. A novel feature of boundary as opposed to initial-value problems in 2+1 is that the d-bar formalism now involves a function in the complex plane which is discontinuous across the real axis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-05T14:39:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "half-plane",
      "d-bar formalism",
      "kpii equation",
      "kadomtsev-petviashvili",
      "initial-boundary value problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.physd.2010.11.005",
      "journal": "Physica D Nonlinear Phenomena",
      "year": 2011,
      "month": "Mar",
      "volume": 240,
      "number": 6,
      "pages": 477
    },
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhyD..240..477M"
    }
  }
}