{
  "annotation_id": "080a0ddc-4126-44b9-a7eb-db76b7bdd3be",
  "date_created": "2026-03-02T18:02:50.965000Z",
  "date_modified": "2026-03-02T18:02:50.965000Z",
  "file_hash": "00436267469451d18466f36fe98d1ca8162b365967b0dc82692e5a120cc854d3",
  "private": false,
  "record": {
    "abstract": "We study the additional symmetries associated with the $q$-deformed\nKadomtsev-Petviashvili ($q$-KP) hierarchy. After identifying the resolvent\noperator as the generator of the additional symmetries, the $q$-KP hierarchy\ncan be consistently reduced to the so-called $q$-deformed constrained KP\n($q$-cKP) hierarchy. We then show that the additional symmetries acting on the\nwave function can be viewed as infinitesimal B\\\"acklund transformations by\nacting the vertex operator on the tau-function of the $q$-KP hierarchy. This\nestablishes the Adler-Shiota-van Moerbeke formula for the $q$-KP hierarchy.",
    "arxiv_id": "solv-int/9811010",
    "authors": [
      "Ming-Hsien Tu"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "journal_ref": "Lett. Math. Phys., 49(2): 95-103, July 1999",
    "title": "Q-deformed KP hierarchy: Its additional symmetries and infinitesimal   B\\\"acklund transformations",
    "url": "https://arxiv.org/abs/solv-int/9811010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a061d516-8782-452a-84bb-a993f150b01c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}