Small planar travelling waves in two-dimensional networks of coupled oscillators |
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| Authors: | Christian Pfrang Karsten Matthies |
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| Affiliation: | 1. Division of Applied Mathematics , Brown University , Providence , RI , USA;2. Department of Mathematical Sciences , University of Bath , Bath, UK |
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| Abstract: | 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. |
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| Keywords: | lattice dynamics infinite-dimensional Hamiltonian dynamics normal forms centre manifold theory travelling waves advance–delay equation |
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