{
  "annotation_id": "c4f5b77a-1c67-4084-8a61-a17240b8ab9e",
  "date_created": "2026-03-02T18:00:28.849000Z",
  "date_modified": "2026-03-02T18:00:28.849000Z",
  "file_hash": "a9a1be9746177f72e43e61608754f042b12ec8e719507c3ce743f0751bf05d4a",
  "private": false,
  "record": {
    "abstract": "By considering the long-wave limit of the regularized long wave (RLW)\nequation, we study its multiple-time higher-order evolution equations. As a\nfirst result, the equations of the Korteweg-de Vries hierarchy are shown to\nplay a crucial role in providing a secularity-free perturbation theory in the\nspecific case of a solitary-wave solution. Then, as a consequence, we show that\nthe related perturbative series can be summed and gives exactly the\nsolitary-wave solution of the RLW equation. Finally, some comments and\nconsiderations are made on the N-soliton solution, as well as on the\nlimitations of applicability of the multiple scale method in obtaining uniform\nperturbative series.",
    "arxiv_id": "patt-sol/9606006",
    "authors": [
      "R. A. Kraenkel",
      "M. A. Manna",
      "V. Merle",
      "J. C. Montero",
      "J. G. Pereira"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.54.2976",
    "title": "Multiple-Time Higher-Order Perturbation Analysis of the Regularized   Long-Wavelength Equation",
    "url": "https://arxiv.org/abs/patt-sol/9606006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ebb945d7-3cad-49c1-bf45-ad6d247d358b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}