{
  "annotation_id": "202f6b2c-57a8-4cfb-a2a5-c8cd46e32e39",
  "date_created": "2026-03-02T18:00:28.660000Z",
  "date_modified": "2026-03-02T18:00:28.660000Z",
  "file_hash": "28a27ebe046cf441375ed5807ae9c15fff295ab115417b6bcd91c804d3803960",
  "private": false,
  "record": {
    "abstract": "We consider initial data for the real Ginzburg-Landau equation having two\nwidely separated zeros. We require these initial conditions to be locally close\nto a stationary solution (the ``kink\u0027\u0027 solution) except for a perturbation\nsupported in a small interval between the two kinks. We show that such a\nperturbation vanishes on a time scale much shorter than the time scale for the\nmotion of the kinks. The consequences of this bound, in the context of earlier\nstudies of the dynamics of kinks in the Ginzburg-Landau equation, [ER], are as\nfollows: we consider initial conditions $v_0$ whose restriction to a bounded\ninterval $I$ have several zeros, not too regularly spaced, and other zeros of\n$v_0$ are very far from $I$. We show that all these zeros eventually disappear\nby colliding with each other. This relaxation process is very slow: it takes a\ntime of order exponential of the length of $I$.",
    "arxiv_id": "patt-sol/9808007",
    "authors": [
      "J. Rougemont"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1088/0951-7715/12/3/007",
    "title": "Dynamics of kinks in the Ginzburg-Landau equation: Approach to a   metastable shape and collapse of embedded pairs of kinks",
    "url": "https://arxiv.org/abs/patt-sol/9808007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "49387903-4773-42d4-a015-84e598b0a3e1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}