{
  "annotation_id": "8afe72f3-a36a-462e-bfd4-6bee490d3c99",
  "date_created": "2026-02-17T05:53:05.049000Z",
  "date_modified": "2026-02-17T05:53:05.049000Z",
  "file_hash": "44ab903e44c4cb3124efda7703a28a6d8d673f2b5b75543d29b6e43944493981",
  "private": false,
  "record": {
    "abstract": "In this paper, we present two new aspects of lattice Boussinesq (BSQ) equations. First, we show that the lattice potential BSQ (lpBSQ) equation defined on a nine-point square lattice admits a natural extension of three-dimensional consistency to a $3\\times 3\\times 3$ cube\\textemdash a cubic sublattice consisting of $27$ vertices. This extends the standard notion of three-dimensional consistency (defined on an elementary $2\\times 2\\times 2$ vertex cube for quadrilateral equations) to the non-quadrilateral, nine-point setting. Second, we construct a new three-component system which is referred to as the {\\em lattice BSQ-Q3 system}, serving as the BSQ analogue of the Q3($\\delta$) equation in the Adler-Bobenko-Suris (ABS) classification. The construction relies on a gauge transformation between Lax pairs of lpBSQ with the parameter $\\delta$ arising from a $GL_3$ action. In a degeneration form, the system yields a $PGL_3$-invariant integrable lattice equation that generalises the $PGL_2$-invariant Schwarzian BSQ equation.",
    "arxiv_id": "2601.05565",
    "authors": [
      "Pengyu Sun",
      "Cheng Zhang",
      "Frank Nijhoff"
    ],
    "categories": [
      "nlin.SI",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On consistency around a $3 \\times 3\\times 3$ cube and Q3 analogue of the lattice Boussinesq equation",
    "url": "https://arxiv.org/abs/2601.05565",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "57209bf3-68c5-4c62-847d-b9bce5224adf",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}