{
  "annotation_id": "c1616527-30a9-4891-a161-32c784974ada",
  "date_created": "2026-03-02T18:00:28.877000Z",
  "date_modified": "2026-03-02T18:00:28.877000Z",
  "file_hash": "447eefd5a15e08bbf37fd8358256e9043165d1137f4c239304cd8f642f4ae7db",
  "private": false,
  "record": {
    "abstract": "We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys.\nJETP {\\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves\nin the nonlinear Schr\\\"oedinger equation (NLS) can be generalised for models\nwith two phase symmetries. MI of three-wave parametric spatial solitons due to\ngroup velocity dispersion (GVD) is investigated as a typical example of such\nmodels. We reveal a new branch of neck instability, which dominates the usual\nsnake type MI found for normal GVD. The resultant nonlinear evolution is\nthereby qualitatively different from cases with only a single phase symmetry.",
    "arxiv_id": "patt-sol/9906005",
    "authors": [
      "Dmitry V. Skryabin",
      "William J. Firth"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevLett.81.3379",
    "journal_ref": "Phys. Rev. Lett., v. 81, pp. 3379-3382 (1998)",
    "title": "Modulational instability of solitary waves in non-degenerate three-wave   mixing: The role of phase symmetries",
    "url": "https://arxiv.org/abs/patt-sol/9906005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fbe41367-accf-4c7e-98df-24837a25a55b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}