{
  "annotation_id": "eb113035-fba1-4fb4-b4ff-20df573c858a",
  "date_created": "2026-03-02T18:02:48.539000Z",
  "date_modified": "2026-03-02T18:02:48.539000Z",
  "file_hash": "e925d2268f20c183207675e68d6b3e6e0065d0d8a94ad7cd3fc98213cb5229db",
  "private": false,
  "record": {
    "abstract": "We propose a general algebraic analytic scheme for the spectral transform of\nsolutions of nonlinear evolution equations. This allows us to give the general\nintegrable evolution corresponding to an arbitrary time and space dependence of\nthe spectral transform (in general nonlinear and with non-analytic dispersion\nrelations). The main theorem is that the compatibility conditions gives always\na true nonlinear evolution because it can always be written as an identity\nbetween polynomials in the spectral variable $k$. This general result is then\nused to obtain first a method to generate a new class of solutions to the\nnonlinear Schroedinger equation, and second to construct the spectral transform\ntheory for solving initial-boundary value problems for resonant wave-coupling\nprocesses (like self-induced transparency in two-level media, or stimulated\nBrillouin scattering of plasma waves or else stimulated Raman scattering in\nnonlinear optics etc...).",
    "arxiv_id": "solv-int/9401004",
    "authors": [
      "Jerome Leon"
    ],
    "categories": [
      "solv-int",
      "nlin.PS",
      "nlin.SI",
      "patt-sol"
    ],
    "doi": "10.1063/1.530426",
    "title": "Nonlinear integrable systems related to arbitrary space-time dependence   of the spectral transform",
    "url": "https://arxiv.org/abs/solv-int/9401004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "01a6da8e-1d75-407d-95ff-509a1641f977",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}