{
  "annotation_id": "a503805a-310f-4cf9-952f-ea73bedb3018",
  "date_created": "2026-03-02T18:02:50.570000Z",
  "date_modified": "2026-03-02T18:02:50.570000Z",
  "file_hash": "a7a949bf4b5a9b233c2b8ab7afa50769903567a53a76293bad764abbd25c743f",
  "private": false,
  "record": {
    "abstract": "In this paper the stability of the Korteweg-de Vries (KdV) equation is\ninvestigated. It is shown analytically and numerically that small perturbations\nof solutions of the KdV-equation introduce effects of dispersion, hence the\nperturbation propagates with a different velocity then the unperturbed\nsolution. This effect is investigated analytically by formulating a\ndifferential equation for perturbations of solutions of the KdV-equation. This\ndifferential equation is solved generally using an Inverse Scattering Technique\n(IST) using the continuous part of the spectrum of the Schr\\\"{o}dinger\nequation. It is shown explicitly that the perturbation consist of two parts.\nThe first part represents the time-evolution of the perturbation only. The\nsecond part represents the interaction between the perturbation and the\nunperturbed solution. It is shown explicitly that singular non-dispersive\nsolutions of the KdV-equation are unstable.",
    "arxiv_id": "solv-int/9605005",
    "authors": [
      "H. J. S. Dorren",
      "R. K. Snieder"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "A stability analysis for the Korteweg-de Vries equation",
    "url": "https://arxiv.org/abs/solv-int/9605005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7e457079-bb9d-4a4e-92df-55c71369b56e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}