{
  "annotation_id": "f13d8df9-ca51-4b49-a018-5f0d9a0276fa",
  "date_created": "2026-03-02T18:02:51.344000Z",
  "date_modified": "2026-03-02T18:02:51.344000Z",
  "file_hash": "2eb858238e09d11fd43dcd24e70b65b081d18d63d2ff3a3ac8b82e90f58cc78a",
  "private": false,
  "record": {
    "abstract": "A detailed analysis of the small-amplitude solutions of a deformed discrete\nnonlinear Schr\\\"{o}dinger equation is performed. For generic deformations the\nsystem possesses \"singular\" points which split the infinite chain in a number\nof independent segments. We show that small-amplitude dark solitons in the\nvicinity of the singular points are described by the Toda-lattice equation\nwhile away from the singular points are described by the Korteweg-de Vries\nequation. Depending on the value of the deformation parameter and of the\nbackground level several kinds of solutions are possible. In particular we\ndelimit the regions in the parameter space in which dark solitons are stable in\ncontrast with regions in which bright pulses on nonzero background are\npossible. On the boundaries of these regions we find that shock waves and\nrapidly spreading solutions may exist.",
    "arxiv_id": "solv-int/9611002",
    "authors": [
      "V. V. Konotop",
      "M. Salerno"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1103/PhysRevE.55.4706",
    "title": "Small-amplitude excitations in a deformable discrete nonlinear   Schroedinger equation",
    "url": "https://arxiv.org/abs/solv-int/9611002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ea518afb-e556-4aae-9da3-636d8898418e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}