{
  "annotation_id": "04a79c88-b969-40ba-bb06-7adc80728177",
  "date_created": "2026-03-02T18:02:51.442000Z",
  "date_modified": "2026-03-02T18:02:51.442000Z",
  "file_hash": "1d9be3225a1ac95c9c4acbcbf2a95a0a012c1782caff2264ceb718d1f3c94535",
  "private": false,
  "record": {
    "abstract": "The Korteweg de Vries (KdV) equation with small dispersion is a model for the\nformation and propagation of dispersive shock waves in one dimension.\nDispersive shock waves in KdV are characterized by the appearance of zones of\nrapid modulated oscillations in the solution of the Cauchy problem with smooth\ninitial data. The modulation in time and space of the amplitudes, the\nfrequencies and the wave-numbers of these oscillations and their interactions\nis approximately described by the $g$-phase Whitham equations. We study the\ninitial value problem for the Whitham equations for a one parameter family of\nmonotone decreasing initial data. We obtain the bifurcation diagram of the\nnumber $g$ of interacting oscillatory zones.",
    "arxiv_id": "solv-int/9707011",
    "authors": [
      "T. Grava"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Bifurcation diagram of a one-parameter family of dispersive waves",
    "url": "https://arxiv.org/abs/solv-int/9707011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "200b5599-7025-44fb-9601-3b0459b8aaaa",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}