{
  "annotation_id": "683c59b0-89e4-4e20-8fc0-1244dc6f2589",
  "date_created": "2026-03-02T18:01:17.710000Z",
  "date_modified": "2026-03-02T18:01:17.710000Z",
  "file_hash": "3e5e5dad01cc93bd96215af0fed890530a73a1c966dd6f8d646b312c5b2191fb",
  "private": false,
  "record": {
    "abstract": "The (Michelson) Sivashinsky equation of premixed flames is studied in a\nrectangular domain in two dimensions. A huge number of 2D stationary solutions\nare trivially obtained by addition of two 1D solutions. With Neumann boundary\nconditions, it is shown numerically that adding two stable 1D solutions leads\nto a 2D stable solution. This type of solution is shown to play an important\nrole in the dynamics of the equation with additive noise.",
    "arxiv_id": "physics/0702099",
    "authors": [
      "Bruno Denet"
    ],
    "categories": [
      "physics.class-ph",
      "nlin.PS",
      "nlin.SI"
    ],
    "doi": "10.1103/PhysRevE.75.046310",
    "journal_ref": "Physical Review E: Statistical, Nonlinear, and Soft Matter Physics\n  75 (2007) 046310",
    "title": "Sivashinsky equation in a rectangular domain",
    "url": "https://arxiv.org/abs/physics/0702099"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c1e73310-ca28-444b-bb24-ef9ef67743d6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}