{
  "annotation_id": "504345ed-dd0a-4b33-84fd-8ec940c39671",
  "date_created": "2026-03-02T18:00:29.152000Z",
  "date_modified": "2026-03-02T18:00:29.152000Z",
  "file_hash": "2fd174db381458154f284c202af8d9a0f1b85c685833248b1ccc86f24746e0bf",
  "private": false,
  "record": {
    "abstract": "We study the generalized Korteweg-DeVries equations derivable from the\nLagrangian: $ L(l,p) = \\int \\left( \\frac{1}{2} \\varphi_{x} \\varphi_{t} - {\n{(\\varphi_{x})^{l}} \\over {l(l-1)}} + \\alpha(\\varphi_{x})^{p}\n(\\varphi_{xx})^{2} \\right) dx, $ where the usual fields $u(x,t)$ of the\ngeneralized KdV equation are defined by $u(x,t) = \\varphi_{x}(x,t)$. For $p$ an\narbitrary continuous parameter $0\u003c p \\leq 2 ,l=p+2$ we find compacton solutions\nto these equations which have the feature that their width is independent of\nthe amplitude. This generalizes previous results which considered $p=1,2$. For\nthe exact compactons we find a relation between the energy, mass and velocity\nof the solitons. We show that this relationship can also be obtained using a\nvariational method based on the principle of least action.",
    "arxiv_id": "patt-sol/9307002",
    "authors": [
      "Avinash Khare",
      "Fred Cooper"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.48.4843",
    "title": "One parameter family of Compacton Solutions in a class of Generalized   Korteweg-DeVries Equations",
    "url": "https://arxiv.org/abs/patt-sol/9307002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "66a6c689-5459-47e6-9301-b5d5069c1069",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}