{
  "annotation_id": "500bf7e1-c70f-4b0c-8f30-42d2aa36f7cd",
  "date_created": "2026-03-02T18:02:51.386000Z",
  "date_modified": "2026-03-02T18:02:51.386000Z",
  "file_hash": "6958ee83d1ffb7d886657fd7b3031276fbf7b75b0f2b5b9844f53dc2a2ce24fb",
  "private": false,
  "record": {
    "abstract": "The acoustic scattering operator on the real line is mapped to a\nSchr\\\"odinger operator under the Liouville transformation. The potentials in\nthe image are characterized precisely in terms of their scattering data, and\nthe inverse transformation is obtained as a simple, linear quadrature. An\nexistence theorem for the associated Harry Dym flows is proved, using the\nscattering method. The scattering problem associated with the Camassa-Holm\nflows on the real line is solved explicitly for a special case, which is used\nto reduce a general class of such problems to scattering problems on finite\nintervals.",
    "arxiv_id": "solv-int/9901007",
    "authors": [
      "R. Beals",
      "D. H. Sattinger",
      "J. Szmigielski"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "journal_ref": "Advances in Mathematics, vol 140, (1998), 190-206",
    "title": "Acoustic Scattering and the Extended Korteweg deVries hierarchy",
    "url": "https://arxiv.org/abs/solv-int/9901007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f237c174-98db-4f60-9aed-65bc31d45e7e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}