dorsal/arxiv
View SchemaGlobal modes for the complex Ginzburg-Landau equation
| Authors | Le S. Dizès |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9502008 |
| URL | https://arxiv.org/abs/patt-sol/9502008 |
Abstract
Linear global modes, which are time-harmonic solutions with vanishing boundary conditions, are analysed in the context of the complex Ginzburg-Landau equation with slowly varying coefficients in doubly infinite domains. The most unstable modes are shown to be characterized by the geometry of their Stokes line network: they are found to generically correspond to a configuration with two turning points issued from opposite sides of the real axis which are either merged or connected by a common Stokes line. A region of local absolute instability is also demonstrated to be a necessary condition for the existence of unstable global modes.
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"date_created": "2026-03-02T18:00:28.614000Z",
"date_modified": "2026-03-02T18:00:28.614000Z",
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"abstract": "Linear global modes, which are time-harmonic solutions with vanishing\nboundary conditions, are analysed in the context of the complex Ginzburg-Landau\nequation with slowly varying coefficients in doubly infinite domains. The most\nunstable modes are shown to be characterized by the geometry of their Stokes\nline network: they are found to generically correspond to a configuration with\ntwo turning points issued from opposite sides of the real axis which are either\nmerged or connected by a common Stokes line. A region of local absolute\ninstability is also demonstrated to be a necessary condition for the existence\nof unstable global modes.",
"arxiv_id": "patt-sol/9502008",
"authors": [
"Le S. Diz\u00e8s"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Global modes for the complex Ginzburg-Landau equation",
"url": "https://arxiv.org/abs/patt-sol/9502008"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "37c109fb-8da3-49a8-b699-c4591e7fbf67",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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