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

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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.
Original languageEnglish
Pages (from-to)157-170
Number of pages14
JournalDynamical Systems: An International Journal
Volume24
Issue number2
DOIs
Publication statusPublished - 2009

Keywords

  • breathers
  • pasta-ulam lattice
  • nonlinear oscillators
  • normal forms
  • centre manifold theory
  • solitary waves
  • discrete
  • chain
  • travelling waves
  • advance-delay equation
  • lattice dynamics
  • infinite-dimensional Hamiltonian dynamics
  • fpu lattices

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