{
  "annotation_id": "c3e03584-dbc2-40c0-8cbc-11d1ecb65129",
  "date_created": "2026-03-02T18:02:50.898000Z",
  "date_modified": "2026-03-02T18:02:50.898000Z",
  "file_hash": "a9e0fc882e587f8c90bb5ab885797ce12dee48c062fe534017c0433ca34e874a",
  "private": false,
  "record": {
    "abstract": "The multiple-scale perturbation theory, well known for long-waves, is\nextended to the study of the far-field behaviour of short-waves, commonly\ncalled ripples. It is proved that the Benjamin-Bona-Mahony- Peregrine equation\ncan propagates short-waves. This result contradict the Benjamin hypothesis that\nshort-waves tends not to propagate in this model and close a part of the old\ncontroversy between Korteweg-de Vries and Benjamin-Bona-Mahony-Peregrine\nequations. We shown that a nonlinear (quadratic) Klein-Gordon type equation\nsubstitutes in a short-wave analysis the ubiquitous Korteweg-de Vries equation\nof long-wave approach. Moreover the kink solutions of phi-4 and sine-Gordon\nequations are understood as an all orders asymptotic behaviour of short-waves.\nIt is proved that the antikink solution of phi-4 model which was never obtained\nperturbatively can be obtained by perturbation expansion in the wave-number k\nin the short-wave limit.",
    "arxiv_id": "solv-int/9710013",
    "authors": [
      "M. A. Manna",
      "V. Merle"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1103/PhysRevE.57.6206",
    "title": "Asymptotic dynamics of short-waves in nonlinear dispersive models",
    "url": "https://arxiv.org/abs/solv-int/9710013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "28251c71-40fc-440b-805c-1fbc516e7c1a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}