{
  "annotation_id": "7ed94d09-5459-423e-9e56-d18be71b7994",
  "date_created": "2026-03-02T18:00:28.606000Z",
  "date_modified": "2026-03-02T18:00:28.606000Z",
  "file_hash": "09a56281fbd1ae7ba9f5a42608fde711c40e8332944ae7e36a25ffd2d6a71f84",
  "private": false,
  "record": {
    "abstract": "The cubic Complex Ginzburg-Landau Equation (CGLE) has a one parameter family\nof traveling localized source solutions. These so called \u0027Nozaki-Bekki holes\u0027\nare (dynamically) stable in some parameter range, but always structually\nunstable: A perturbation of the equation in general leads to a (positive or\nnegative) monotonic acceleration or an oscillation of the holes. This confirms\nthat the cubic CGLE has an inner symmetry. As a consequence small perturbations\nchange some of the qualitative dynamics of the cubic CGLE and enhance or\nsuppress spatio-temporal intermittency in some parameter range. An analytic\nstability analysis of holes in the cubic CGLE and a semianalytical treatment of\nthe acceleration instability in the perturbed equation is performed by using\nmatching and perturbation methods. Furthermore we treat the asymptotic\nhole-shock interaction. The results, which can be obtained fully analytically\nin the nonlinear Schroedinger limit, are also used for the quantitative\ndescription of modulated solutions made up of periodic arrangements of\ntraveling holes and shocks.",
    "arxiv_id": "patt-sol/9409002",
    "authors": [
      "Stefan Popp",
      "Olaf Stiller",
      "Igor Aranson",
      "Lorenz Kramer"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1016/0167-2789(95)00070-K",
    "title": "Hole Solutions in the 1d Complex Ginzburg-Landau Equation",
    "url": "https://arxiv.org/abs/patt-sol/9409002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e4c4c426-4b31-4a24-854a-2bf6fc2edda0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}