{
  "annotation_id": "82af2f8c-7246-4404-baf4-ded19c417bb7",
  "date_created": "2026-03-02T18:00:28.845000Z",
  "date_modified": "2026-03-02T18:00:28.845000Z",
  "file_hash": "d89f5a4a1655167dfce0ae4e35de0dd55157f7cbb4e2d4007858b16dd1ab619f",
  "private": false,
  "record": {
    "abstract": "By using the multiple scale method with the simultaneous introduction of\nmultiple times, we study the propagation of long surface-waves in a shallow\ninviscid fluid. As a consequence of the requirements of scale invariance and\nabsence of secular terms in each order of the perturbative expansion, we show\nthat the Korteweg-de Vries hierarchy equations do appear in the description of\nsuch waves. Finally, we show that this procedure of eliminating secularities is\nclosely related to the renormalization technique introduced by Kodama and\nTaniuti.",
    "arxiv_id": "patt-sol/9406001",
    "authors": [
      "R. A. Kraenkel",
      "M. A. Manna",
      "J. G. Pereira"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS",
      "nlin.SI",
      "solv-int"
    ],
    "doi": "10.1063/1.531294",
    "title": "The Korteweg-de Vries Hierarchy and Long Water-Waves",
    "url": "https://arxiv.org/abs/patt-sol/9406001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0a58321c-ff5b-4b57-b6bc-611bd7afb674",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}