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

摘要

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.