{
  "annotation_id": "364f7cdf-c77c-4e7e-b8d2-6cd6b9d4cc6d",
  "date_created": "2026-03-02T18:02:48.236000Z",
  "date_modified": "2026-03-02T18:02:48.236000Z",
  "file_hash": "3195c4a504580858cd724374ce7a4c549de76995529e47c7847c19344c84da84",
  "private": false,
  "record": {
    "abstract": "The solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with\ngiven initial data $u(0,x,y)$ belonging to the Schwartz space is considered. No\nadditional special constraints, usually considered in literature, as\n$\\int\\!dx\\,u(0,x,y)=0$ are required to be satisfied by the initial data. The\nproblem is completely solved in the framework of the spectral transform theory\nand it is shown that $u(t,x,y)$ satisfies a special evolution version of the\nKPI equation and that, in general, $\\partial_t u(t,x,y)$ has different left and\nright limits at the initial time $t=0$. The conditions of the type\n$\\int\\!dx\\,u(t,x,y)=0$, $\\int\\!dx\\,xu_y(t,x,y)=0$ and so on (first, second,\netc. `constraints\u0027) are dynamically generated by the evolution equation for\n$t\\not=0$. On the other side $\\int\\!dx\\!\\!\\int\\!dy\\,u(t,x,y)$ with prescribed\norder of integrations is not necessarily equal to zero and gives a nontrivial\nintegral of motion.",
    "arxiv_id": "solv-int/9306004",
    "authors": [
      "M. Boiti",
      "F. Pempinelli",
      "A. Pogrebkov"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1088/0266-5611/10/3/001",
    "title": "Solutions of the Kpi Equation with Smooth Initial Data",
    "url": "https://arxiv.org/abs/solv-int/9306004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b156a412-895b-42c5-9a8d-d12734067d45",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}