{
  "id": "1802.07676",
  "version": "v1",
  "published": "2018-02-21T17:18:52.000Z",
  "updated": "2018-02-21T17:18:52.000Z",
  "title": "Nonlinear stability of source defects in oscillatory media",
  "authors": [
    "Margaret Beck",
    "Toan T. Nguyen",
    "Björn Sandstede",
    "Kevin Zumbrun"
  ],
  "comment": "43 pages, 5 figures",
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects are important as organizing centers of more complicated flows. Our analysis uses spatial dynamics combined with an instantaneous phase-tracking technique to obtain detailed pointwise estimates describing perturbations to lowest order as a phase-shift radiating outward at a linear rate plus a pair of localized approximately Gaussian excitations along the phase-shift boundaries; we show that in the wake of these outgoing waves the perturbed solution converges time-exponentially to a space-time translate of the original source pattern.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-21T17:18:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear stability",
      "oscillatory media",
      "emits periodic wave trains",
      "spectrally stable time-periodic source defects",
      "linear rate plus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}