{
  "annotation_id": "f0845a52-4480-4ab6-8ddc-a2fa18e2896e",
  "date_created": "2026-03-02T18:00:28.668000Z",
  "date_modified": "2026-03-02T18:00:28.668000Z",
  "file_hash": "ae762f689f0502d0448dfbe1ca373bbc2a8283b621ec3016e2024dfb0ce4dc5b",
  "private": false,
  "record": {
    "abstract": "Using the method of separation of variables, we developed a vector\nnonparaxial theory for the nonlinear wave equations in strong field\napproximation. We found that exact localized vortex soliton solution exists for\nthe nonlinear 3D+1 vector wave equation and for 3D+1 vector nonlinear\nSchr\\\"{o}dinger equation. This method is applicable for angular functions,\nwhich satisfy additional conditions. It is shown that exact vortex solitary\nwave exists only for solution with eigenvalue of momentum L=1",
    "arxiv_id": "patt-sol/9902008",
    "authors": [
      "L. M. Kovachev"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "title": "Three dimensional bright vortex soliton",
    "url": "https://arxiv.org/abs/patt-sol/9902008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "505e0f9d-0e60-4e8f-93ce-aff3fd575921",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}