dorsal/arxiv
View SchemaOn the degenerated soft-mode instability
| Authors | Wolfram Just, Frank Matthäus, Herwig Sauermann |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9808002 |
| URL | https://arxiv.org/abs/patt-sol/9808002 |
| DOI | 10.1088/0305-4470/31/28/008 |
Abstract
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general equation of motion the full amplitude equation is derived systematically and formulas for the dependence of the coefficients on the system parameters are obtained. We emphasise the importance of nonlinear derivative terms in the amplitude equation for the behaviour in the vicinity of the bifurcation point. Especially the numerical values of the corresponding coefficients determine the region of coexistence between the stable trivial solution and stable spatially periodic patterns. Our approach clearly shows that similar considerations fail for the case of oscillatory instabilities.
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"abstract": "We consider instabilities of a single mode with finite wavenumber in\ninversion symmetric spatially one dimensional systems, where the character of\nthe bifurcation changes from sub- to supercritical behaviour. Starting from a\ngeneral equation of motion the full amplitude equation is derived\nsystematically and formulas for the dependence of the coefficients on the\nsystem parameters are obtained. We emphasise the importance of nonlinear\nderivative terms in the amplitude equation for the behaviour in the vicinity of\nthe bifurcation point. Especially the numerical values of the corresponding\ncoefficients determine the region of coexistence between the stable trivial\nsolution and stable spatially periodic patterns. Our approach clearly shows\nthat similar considerations fail for the case of oscillatory instabilities.",
"arxiv_id": "patt-sol/9808002",
"authors": [
"Wolfram Just",
"Frank Matth\u00e4us",
"Herwig Sauermann"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1088/0305-4470/31/28/008",
"title": "On the degenerated soft-mode instability",
"url": "https://arxiv.org/abs/patt-sol/9808002"
},
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