{
  "annotation_id": "4302aaa3-edc0-41b4-9707-45b2b1650e89",
  "date_created": "2026-03-02T18:02:51.575000Z",
  "date_modified": "2026-03-02T18:02:51.575000Z",
  "file_hash": "dc079b5d178bc7e1da6346b916860150b0cf36353b5720ff0252417ecac0ee61",
  "private": false,
  "record": {
    "abstract": "We consider the $m$-phase Whitham\u0027s averaging method and propose a procedure\nof \"averaging\" of non-local Hamiltonian structures. The procedure is based on\nthe existence of a sufficient number of local commuting integrals of a system\nand gives a Poisson bracket of Ferapontov type for the Whitham\u0027s system. The\nmethod can be considered as a generalization of the Dubrovin-Novikov procedure\nfor the local field-theoretical brackets.",
    "arxiv_id": "solv-int/9910011",
    "authors": [
      "Andrei Ya. Maltsev"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "journal_ref": "Intern. Journ. of Math. and Math. Sci. 30:7 (2002) 399-434",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The averaging of non-local Hamiltonian structures in Whitham\u0027s method",
    "url": "https://arxiv.org/abs/solv-int/9910011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c96e7d27-1423-4b14-9c32-15ac4e1f294b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}