{
  "annotation_id": "19312166-8156-4baf-ad78-e06aaeabd678",
  "date_created": "2026-03-02T18:02:50.758000Z",
  "date_modified": "2026-03-02T18:02:50.758000Z",
  "file_hash": "79c6ab8d96fe254b67cc0bd3cc55e527806445f377258e75db08b8649f47aaa4",
  "private": false,
  "record": {
    "abstract": "We present here the iteration procedure for the determination of free energy\n$\\epsilon^{2}$-expansion using the theory of KdV - type equations. In our\napproach we use the conservation laws for KdV - type equations depending\nexplicitly on times $t_{1}, t_{2}, ...$ to find the $\\epsilon^{2}$-expansion of\n$u(x,t_{1},t_{2},...)$ after the infinite number of shifts of $u(x,0,0,...)\n\\equiv x$ along $t_{1}, t_{2}, ...$ in recurrent form. The formulas for the\nfree energy expansion are just obtained then as a result of quite simple\nintegration procedure applied to $u_{n}(x)$.",
    "arxiv_id": "solv-int/9904004",
    "authors": [
      "B. A. Dubrovin",
      "A. Ya. Maltsev"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "nlin.SI"
    ],
    "title": "Recurrent procedure for the determination of the Free Energy   $\\epsilon^{2}$-expansion in the Topological String Theory",
    "url": "https://arxiv.org/abs/solv-int/9904004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b9651553-e1dd-4ae8-a8c9-692ad21b27fe",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}