{
  "annotation_id": "d15eb130-a9f3-4723-8b4a-b8d1e708f18c",
  "date_created": "2026-03-02T18:01:52.618000Z",
  "date_modified": "2026-03-02T18:01:52.618000Z",
  "file_hash": "88bbf95164dd87fde10a467e17954b1fd9e66bd943e0f5eaa59113424effe0f7",
  "private": false,
  "record": {
    "abstract": "The matrix 2x2 spectral differential equation of the second order is\nconsidered on x in ($-\\infty,+\\infty$). We establish elementary Darboux\ntransformations covariance of the problem and analyze its combinations. We\nselect a second covariant equation to form Lax pair of a coupled KdV-MKdV\nsystem. The sequence of the elementary Darboux transformations of the\nzero-potential seed produce two-parameter solution for the coupled KdV-MKdV\nsystem with reductions. We show effects of parameters on the resulting\nsolutions (reality, singularity). A numerical method for general coupled\nKdV-MKdV system is introduced. The method is based on a difference scheme for\nCauchy problems for arbitrary number of equations with constants coefficients.\nWe analyze stability and prove the convergence of the scheme which is also\ntested by numerical simulation of the explicit solutions.",
    "arxiv_id": "quant-ph/0210003",
    "authors": [
      "A. Halim",
      "S. Kshevetskii",
      "S. Leble"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Analytical and numerical solution of coupled KdV-MKdV system",
    "url": "https://arxiv.org/abs/quant-ph/0210003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "29a84a28-ab2e-44c9-ab10-11f5ed2af78e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}