{
  "annotation_id": "4ac6c2a5-f026-496b-b051-b13fb58ce5f1",
  "date_created": "2026-03-02T18:02:31.202000Z",
  "date_modified": "2026-03-02T18:02:31.202000Z",
  "file_hash": "2cf68f3e25f97a3afe00a3714b97688c6527de08586020ddb27b228e60818562",
  "private": false,
  "record": {
    "abstract": "A useful semiclassical method to calculate eigenfunctions of the Schroedinger\nequation is the mapping to a well-known ordinary differential equation, as for\nexample Airy\u0027s equation. In this paper we generalize the mapping procedure to\nthe nonlinear Schroedinger equation or Gross-Pitaevskii equation describing the\nmacroscopic wave function of a Bose-Einstein condensate. The nonlinear\nSchroedinger equation is mapped to the second Painleve equation, which is one\nof the best-known differential equations with a cubic nonlinearity. A\nquantization condition is derived from the connection formulae of these\nfunctions. Comparison with numerically exact results for a harmonic trap\ndemonstrates the benefit of the mapping method. Finally we discuss the\ninfluence of a shallow periodic potential on bright soliton solutions by a\nmapping to a constant potential.",
    "arxiv_id": "quant-ph/0608099",
    "authors": [
      "D. Witthaut",
      "H. J. Korsch"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/39/47/012",
    "journal_ref": "J. Phys. A: Math. Gen. 39, 14687 (2006)",
    "title": "Uniform semiclassical approximations of the nonlinear Schroedinger   equation by a Painleve mapping",
    "url": "https://arxiv.org/abs/quant-ph/0608099"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c1cba9c5-c96f-4446-bd58-a93073454ff9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}