Stable transport of information near essentially unstable localized structures

  title={Stable transport of information near essentially unstable localized structures},
  author={Thierry Gallay and Guido Schneider and Hannes Uecker},
  journal={Discrete and Continuous Dynamical Systems-series B},
When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B. Sandstede and A. Scheel for a class of reaction-diffusion systems on the real line. Under general assumptions, they showed that the modulated fronts exist and are spectrally stable near the bifurcation point. Here we consider a model problem for which we can prove… 
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  • B. Sandstede, A. Scheel
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1999
Reaction-diffusion systems on the real line are considered. Localized travelling waves become unstable when the essential spectrum of the linearization about them crosses the imaginary axis. In this
Spectral stability of modulated travelling waves bifurcating near essential instabilities
  • B. Sandstede, A. Scheel
  • Physics, Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2000
Localized travelling waves to reaction-diffusion systems on the real line are investigated. The issue addressed in this work is the transition to instability which arises when the essential spectrum
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Various instability mechanisms of fronts in reaction-diffusion systems are analysed; the emphasis is on instabilities that have the potential to create modulated (i.e. time-periodic) waves near the
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Modulated travelling waves are solutions to reaction-diffusion equations that are time-periodic in an appropriate moving coordinate frame. They may arise through Hopf bifurcations or essential
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