{
  "annotation_id": "c1bf10b2-402d-4174-bd15-97782a466adc",
  "date_created": "2026-03-02T18:02:51.273000Z",
  "date_modified": "2026-03-02T18:02:51.273000Z",
  "file_hash": "dd740e2266b3caaa0a67660c1120f04a6f3abf71cf93e6dc0158f141af3ec802",
  "private": false,
  "record": {
    "abstract": "The asymptotic solution for the Painleve-2 equation with small parameter is\nconsidered. The solution has algebraic behavior before point $t_*$ and fast\noscillating behavior after the point $t_*$. In the transition layer the\nbehavior of the asymptotic solution is more complicated. The leading term of\nthe asymptotics satisfies the Painleve-1 equation and some elliptic equation\nwith constant coefficients, where the solution of the Painleve-1 equation has\npoles. The uniform smooth asymptotics are constructed in the interval,\ncontaining the critical point $t_*$.",
    "arxiv_id": "solv-int/9902007",
    "authors": [
      "O. M. Kiselev"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Asymptotic approach for the rigid condition of appearance of the   oscillations in the solution of the Painleve-2 equation",
    "url": "https://arxiv.org/abs/solv-int/9902007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "39d88100-9ce0-4323-8523-5e5a455a1d5d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}