{
  "annotation_id": "b7bb5343-31e6-4fff-a988-1bb70b67caf1",
  "date_created": "2026-03-02T18:00:29.460000Z",
  "date_modified": "2026-03-02T18:00:29.460000Z",
  "file_hash": "9a1e7bf15fd14537e5f43a3ab200f35a78d4419f0b550c8953de7d6126b19d6e",
  "private": false,
  "record": {
    "abstract": "It is shown that the renormalization group (RG) method for global analysis\ncan be formulated in the context of the classical theory of envelopes: Several\nexamples from partial differential equations are analyzed. The amplitude\nequations which are usually derived by the reductive perturbation theory are\nshown to be naturally derived as the equations describing the envelopes of the\nlocal solutions obtained in the perturbation theory.",
    "arxiv_id": "patt-sol/9508001",
    "authors": [
      "Teiji Kunihiro"
    ],
    "categories": [
      "patt-sol",
      "chao-dyn",
      "cond-mat",
      "funct-an",
      "math.FA",
      "nlin.CD",
      "nlin.PS"
    ],
    "title": "A Geometrical Formulation of the Renormalization Group Method for Global   Analysis II: Partial Differential Equations",
    "url": "https://arxiv.org/abs/patt-sol/9508001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "76f5813b-68b3-464a-ae2e-5b7a69cc8e0c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}