{
  "annotation_id": "0fcbdd6a-4573-4df3-a5d2-eecb1e34b35b",
  "date_created": "2026-03-02T18:02:50.568000Z",
  "date_modified": "2026-03-02T18:02:50.568000Z",
  "file_hash": "31fd28320c1e9f4b5db3eee8e2a992e529d96406d8af5fdc580d5e636b35ae21",
  "private": false,
  "record": {
    "abstract": "We obtain the classification of integrable equations of the form\n$u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$ using the formal symmetry method of Mikhailov\net al [A.V.Mikhailov, A.B.Shabat and V.V.Sokolov, in {\\it What is\nIntegrability} edited by V.E. Zakharov (Springer-Verlag, Berlin 1991)]. We show\nthat all such equations can be transformed to an integrable equation of the\nform $v_t=v_{xxx}+f(v,v_x,v_{xx})$ using transformations\n$\\Phi(x,t,u,v,u_x,v_x)=0$, and the $u_{xx}$ dependence can be eliminated except\nfor two equations.",
    "arxiv_id": "solv-int/9605004",
    "authors": [
      "Ayse Humeyra Bilge"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Classification of Integrable Evolution Equations of the Form   $u_t=u_{xxx}+f(t,x,u,u_x,u_{xx})$",
    "url": "https://arxiv.org/abs/solv-int/9605004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "54cdba04-788f-4c39-ba12-22d7ceefb2a2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}