Small planar travelling waves in two-dimensional networks of coupled oscillators

The existence of several small planar travelling waves with arbitrary direction of propagation is shown for two-dimensional cubic networks of oscillators with linear nearest-neighbour coupling. The analysis is based on a spatial dynamics reformulation of the relevant advance-delay equation. Whereas...

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Bibliographic Details
Published inDynamical systems (London, England) Vol. 24; no. 2; pp. 157 - 170
Main Authors Pfrang, Christian, Matthies, Karsten
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.06.2009
Subjects
advance-delay equation
centre manifold theory
infinite-dimensional Hamiltonian dynamics
lattice dynamics
normal forms
travelling waves
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Summary:The existence of several small planar travelling waves with arbitrary direction of propagation is shown for two-dimensional cubic networks of oscillators with linear nearest-neighbour coupling. The analysis is based on a spatial dynamics reformulation of the relevant advance-delay equation. Whereas important aspects of the analysis are discontinuous in the direction of travel, and continuity of the travelling wave is shown with respect to the direction.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1468-9367
1468-9375
DOI:10.1080/14689360802541281