{
  "id": "1510.06913",
  "version": "v1",
  "published": "2015-10-23T12:31:13.000Z",
  "updated": "2015-10-23T12:31:13.000Z",
  "title": "Grassmann extensions of Yang-Baxter maps",
  "authors": [
    "Georgi G. Grahovski",
    "Sotiris Konstantinou-Rizos",
    "Alexander V. Mikhailov"
  ],
  "comment": "16 pages, LaTeX",
  "categories": [
    "nlin.SI",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we show that there are explicit Yang-Baxter maps with Darboux-Lax representation between Grassman extensions of algebraic varieties. Motivated by some recent results on noncommutative extensions of Darboux transformations, we first derive a Darboux matrix associated with the Grassmann-extended derivative Nonlinear Schrodinger (DNLS) equation, and then we deduce novel endomorphisms of Grassmann varieties, which possess the Yang-Baxter property. In particular, we present ten-dimensional maps which can be restricted to eight-dimensional Yang-Baxter maps on invariant leaves, related to the Grassmann-extended NLS and DNLS equations. We consider their vector generalisations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-23T12:31:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grassmann extensions",
      "explicit yang-baxter maps",
      "eight-dimensional yang-baxter maps",
      "deduce novel endomorphisms",
      "derivative nonlinear schrodinger"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/49/14/145202"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1401101
    }
  }
}