{
  "annotation_id": "affdc0c5-2d5e-47a9-b9e1-49c55b2c8cd7",
  "date_created": "2026-03-02T18:02:51.455000Z",
  "date_modified": "2026-03-02T18:02:51.455000Z",
  "file_hash": "41e1cfb1e487fb6bdf5ea945a9d036ce348e84bd0a5b317c061a9e0fc97131e5",
  "private": false,
  "record": {
    "abstract": "Uniform estimates for the decay structure of the $n$-soliton solution of the\nKorteweg-deVries equation are obtained. The KdV equation, linearized at the\n$n$-soliton solution is investigated in a class $\\WW$ consisting of sums of\ntravelling waves plus an exponentially decaying residual term. An analog of the\nkernel of the time-independent equation is proposed, leading to solvability\nconditions on the inhomogeneous term. Estimates on the inversion of the\nlinearized KdV equation at the $n$-soliton are obtained.",
    "arxiv_id": "solv-int/9808014",
    "authors": [
      "M. Haragus-Courcelle",
      "D. H. Sattinger"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1007/s000000050101",
    "journal_ref": "Zeit fur Angew. Math. und Physik (ZAMP), vol 49, (1998), pp.\n  436-469",
    "title": "Inversion of the linearized Korteweg-deVries equation at the   multi-soliton solutions",
    "url": "https://arxiv.org/abs/solv-int/9808014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3a984cdc-3f33-46a1-a6f5-18e70b801b07",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}