{
  "annotation_id": "897d4991-4121-4924-ae1c-a09451db7672",
  "date_created": "2026-03-02T18:02:51.408000Z",
  "date_modified": "2026-03-02T18:02:51.408000Z",
  "file_hash": "246bf78f6194d14b795acf7ba38ef6e642c1bcbf8979cd71b91633a2c72b832b",
  "private": false,
  "record": {
    "abstract": "We study characteristic Cauchy problems for the Korteweg-deVries (KdV)\nequation $u_t=uu_x+u_{xxx}$, and the Kadomtsev-Petviashvili (KP) equation\n$u_{yy}=\\bigl(u_{xxx}+uu_x+u_t\\bigr)_x$ with holomorphic initial data\npossessing nonnegative Taylor coefficients around the origin. For the KdV\nequation with initial value $u(0,x)=u_0(x)$, we show that there is no solution\nholomorphic in any neighbourhood of $(t,x)=(0,0)$ in ${\\mathbb C}^2$ unless\n$u_0(x)=a_0+a_1x$. This also furnishes a nonexistence result for a class of\n$y$-independent solutions of the KP equation. We extend this to $y$-dependent\ncases by considering initial values given at $y=0$, $u(t,x,0)=u_0(x,t)$,\n$u_y(t,x,0)=u_1(x,t)$, where the Taylor coefficients of $u_0$ and $u_1$ around\n$t=0$, $x=0$ are assumed nonnegative. We prove that there is no holomorphic\nsolution around the origin in ${\\mathbb C}^3$ unless $u_0$ and $u_1$ are\npolynomials of degree 2 or lower.",
    "arxiv_id": "solv-int/9905010",
    "authors": [
      "Nalini Joshi",
      "Johannes A. Petersen",
      "Luke M. Schubert"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Nonexistence results for the Korteweg-deVries and Kadomtsev-Petviashvili   equations",
    "url": "https://arxiv.org/abs/solv-int/9905010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "16651596-1422-4927-a30f-e64279833960",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}