dorsal/arxiv
View SchemaTangent Bifurcation of Band Edge Plane Waves, Dynamical Symmetry Breaking and Vibrational Localization
| Authors | Sergej Flach |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9509002 |
| URL | https://arxiv.org/abs/patt-sol/9509002 |
| DOI | 10.1016/0167-2789(95)00267-7 |
Abstract
We study tangent bifurcation of band edge plane waves in nonlinear Hamiltonian lattices. The lattice is translationally invariant. We argue for the breaking of permutational symmetry by the new bifurcated periodic orbits. The case of two coupled oscillators is considered as an example for the perturbation analysis, where the symmetry breaking can be traced using Poincare maps. Next we consider a lattice and derive the dependence of the bifurcation energy on the parameters of the Hamiltonian function in the limit of large system sizes. A necessary condition for the occurence of the bifurcation is the repelling of the band edge plane wave's frequency from the linear spectrum with increasing energy. We conclude that the bifurcated orbits will consequently exponentially localize in the configurational space.
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"date_created": "2026-03-02T18:00:29.447000Z",
"date_modified": "2026-03-02T18:00:29.447000Z",
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"abstract": "We study tangent bifurcation of band edge plane waves in nonlinear\nHamiltonian lattices. The lattice is translationally invariant. We argue for\nthe breaking of permutational symmetry by the new bifurcated periodic orbits.\nThe case of two coupled oscillators is considered as an example for the\nperturbation analysis, where the symmetry breaking can be traced using Poincare\nmaps. Next we consider a lattice and derive the dependence of the bifurcation\nenergy on the parameters of the Hamiltonian function in the limit of large\nsystem sizes. A necessary condition for the occurence of the bifurcation is the\nrepelling of the band edge plane wave\u0027s frequency from the linear spectrum with\nincreasing energy. We conclude that the bifurcated orbits will consequently\nexponentially localize in the configurational space.",
"arxiv_id": "patt-sol/9509002",
"authors": [
"Sergej Flach"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/0167-2789(95)00267-7",
"title": "Tangent Bifurcation of Band Edge Plane Waves, Dynamical Symmetry Breaking and Vibrational Localization",
"url": "https://arxiv.org/abs/patt-sol/9509002"
},
"schema_id": "dorsal/arxiv",
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