{
  "annotation_id": "c0482d28-c014-45a6-b40b-1d84c9174a40",
  "date_created": "2026-03-02T18:00:32.483000Z",
  "date_modified": "2026-03-02T18:00:32.483000Z",
  "file_hash": "98f0a87d53629407430c4802f06f3904e04e041b9cb5c4131ad51ec6546f98b4",
  "private": false,
  "record": {
    "abstract": "We present applications of variational -- wavelet approach to three different\nmodels of nonlinear beam motions with underlying collective behaviour:\nVlasov-Maxwell-Poisson systems, envelope dynamics, beam-beam model. We have the\nrepresentation for dynamical variables as a multiresolution (multiscales)\nexpansion via high-localized nonlinear eigenmodes in the base of compactly\nsupported wavelet bases. Numerical modelling demonstrates formation of coherent\nstructures and stable patterns.",
    "arxiv_id": "physics/0101007",
    "authors": [
      "Antonina N. Fedorova",
      "Michael G. Zeitlin"
    ],
    "categories": [
      "physics.acc-ph",
      "math-ph",
      "math.MP",
      "nlin.PS",
      "physics.comp-ph",
      "quant-ph"
    ],
    "title": "Localized Coherent Structures and Patterns Formation in Collective   Models of Beam Motion",
    "url": "https://arxiv.org/abs/physics/0101007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "acea09be-c8f1-41b9-93e1-24a70ffb1573",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}