dorsal/arxiv
View SchemaLocalized Structures in Nonlinear Lattices with Diffusive Coupling and External Driving
| Authors | Igor Mitkov, Konstantin Kladko, A. R. Bishop |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9812008 |
| URL | https://arxiv.org/abs/patt-sol/9812008 |
Abstract
We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to a homogeneous state or nucleating a pair of oppositely moving fronts. The corresponding bifurcation diagram demonstrates a cusp singularity. The obtained analytic results are in good quantitative agreement with numerical simulations.
{
"annotation_id": "bf12a8cd-bf62-4d3f-a48c-c8ec0acc0356",
"date_created": "2026-03-02T18:00:28.669000Z",
"date_modified": "2026-03-02T18:00:28.669000Z",
"file_hash": "207921a5ccc6551fb4c46a9caf2bbf840329a17f5c4c6170e8b77010fc8ebd07",
"private": false,
"record": {
"abstract": "We study the stabilization of localized structures by discreteness in\none-dimensional lattices of diffusively coupled nonlinear sites. We find that\nin an external driving field these structures may lose their stability by\neither relaxing to a homogeneous state or nucleating a pair of oppositely\nmoving fronts. The corresponding bifurcation diagram demonstrates a cusp\nsingularity. The obtained analytic results are in good quantitative agreement\nwith numerical simulations.",
"arxiv_id": "patt-sol/9812008",
"authors": [
"Igor Mitkov",
"Konstantin Kladko",
"A. R. Bishop"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Localized Structures in Nonlinear Lattices with Diffusive Coupling and External Driving",
"url": "https://arxiv.org/abs/patt-sol/9812008"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "cc5a296d-47c3-40c7-853f-1326ae64267c",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}