dorsal/arxiv
View SchemaA domain wall between single-mode and bimodal states and its transition to dynamical behavior in inhomogeneous systems
| Authors | M. van Hecke, B. A. Malomed |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9609003 |
| URL | https://arxiv.org/abs/patt-sol/9609003 |
| DOI | 10.1016/S0167-2789(96)00211-4 |
Abstract
We consider domain walls (DW's) between single-mode and bimodal states that occur in coupled nonlinear diffusion (NLD), real Ginzburg-Landau (RGL), and complex Ginzburg-Landau (CGL) equations with a spatially dependent coupling coefficient. Group-velocity terms are added to the NLD and RGL equations, which breaks the variational structure of these models. In the simplest case of two coupled NLD equations, we reduce the description of stationary configurations to a single second-order ordinary differential equation. We demonstrate analytically that a necessary condition for existence of a stationary DW is that the group-velocity must be below a certain threshold value. Above this threshold, dynamical behavior sets in, which we consider in detail. In the CGL equations, the DW may generate spatio-temporal chaos, depending on the nonlinear dispersion.
{
"annotation_id": "6b32f1d3-2fa7-4814-9862-8ae85fbe47a3",
"date_created": "2026-03-02T18:00:29.153000Z",
"date_modified": "2026-03-02T18:00:29.153000Z",
"file_hash": "5e2923dc305a6b5d610c15ffe1f39552da6ad21b639518e5570b12ecc8777def",
"private": false,
"record": {
"abstract": "We consider domain walls (DW\u0027s) between single-mode and bimodal states that\noccur in coupled nonlinear diffusion (NLD), real Ginzburg-Landau (RGL), and\ncomplex Ginzburg-Landau (CGL) equations with a spatially dependent coupling\ncoefficient. Group-velocity terms are added to the NLD and RGL equations, which\nbreaks the variational structure of these models. In the simplest case of two\ncoupled NLD equations, we reduce the description of stationary configurations\nto a single second-order ordinary differential equation. We demonstrate\nanalytically that a necessary condition for existence of a stationary DW is\nthat the group-velocity must be below a certain threshold value. Above this\nthreshold, dynamical behavior sets in, which we consider in detail. In the CGL\nequations, the DW may generate spatio-temporal chaos, depending on the\nnonlinear dispersion.",
"arxiv_id": "patt-sol/9609003",
"authors": [
"M. van Hecke",
"B. A. Malomed"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/S0167-2789(96)00211-4",
"title": "A domain wall between single-mode and bimodal states and its transition to dynamical behavior in inhomogeneous systems",
"url": "https://arxiv.org/abs/patt-sol/9609003"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "fd749cfc-0d2d-47b7-b2e6-c362290b3ed6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}