{
  "annotation_id": "89e48d33-145c-4cfb-ac7e-b8eae9d9d12a",
  "date_created": "2026-03-02T18:02:51.152000Z",
  "date_modified": "2026-03-02T18:02:51.152000Z",
  "file_hash": "7a05e21cc9af189e2b4ca104bb834c875e7bc547ff567f4d3d2a2288b470e9c6",
  "private": false,
  "record": {
    "abstract": "We suggest a method for integrating sub-families of a family of nonlinear\n{\\sc Schr\\\"odinger} equations proposed by {\\sc H.-D.~Doebner} and {\\sc\nG.A.~Goldin} in the 1+1 dimensional case which have exceptional {\\sc Lie}\nsymmetries. Since the method of integration involves non-local transformations\nof dependent and independent variables, general solutions obtained include\nimplicitly determined functions. By properly specifying one of the arbitrary\nfunctions contained in these solutions, we obtain broad classes of explicit\nsquare integrable solutions. The physical significance and some analytical\nproperties of the solutions obtained are briefly discussed.",
    "arxiv_id": "solv-int/9510001",
    "authors": [
      "P. Nattermann",
      "R. Zhdanov"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "nlin.SI",
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/29/11/021",
    "journal_ref": "J.Phys.A29:2869-2886,1996",
    "title": "On Integrable Doebner-Goldin Equations",
    "url": "https://arxiv.org/abs/solv-int/9510001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1407a372-4c29-4baa-83e9-0b76982934d2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}