{
  "annotation_id": "58a74a89-2ee7-4bc9-b5d7-c0d50511ad81",
  "date_created": "2026-03-02T18:00:28.848000Z",
  "date_modified": "2026-03-02T18:00:28.848000Z",
  "file_hash": "3869e4ea3bcde8930939eededc3498eccacc1596639abcc558d1be9c5dd5a705",
  "private": false,
  "record": {
    "abstract": "We have examined the dynamical behavior of the kink solutions of the\none-dimensional sine-Gordon equation in the presence of a spatially periodic\nparametric perturbation. Our study clarifies and extends the currently\navailable knowledge on this and related nonlinear problems in four directions.\nFirst, we present the results of a numerical simulation program which are not\ncompatible with the existence of a radiative threshold, predicted by earlier\ncalculations. Second, we carry out a perturbative calculation which helps\ninterpret those previous predictions, enabling us to understand in depth our\nnumerical results. Third, we apply the collective coordinate formalism to this\nsystem and demonstrate numerically that it accurately reproduces the observed\nkink dynamics. Fourth, we report on a novel occurrence of length scale\ncompetition in this system and show how it can be understood by means of linear\nstability analysis. Finally, we conclude by summarizing the general physical\nframework that arises from our study.",
    "arxiv_id": "patt-sol/9401005",
    "authors": [
      "Angel Sanchez",
      "A R Bishop",
      "Francisco Dominguez-Adame"
    ],
    "categories": [
      "patt-sol",
      "cond-mat",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.49.4603",
    "title": "Kink stability, propagation, and length scale competition in the   periodically modulated sine-Gordon equation",
    "url": "https://arxiv.org/abs/patt-sol/9401005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bf043695-ef5c-42a2-af07-56ec323d5c03",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}