Stable transport of information near essentially unstable localized structures

@article{Gallay2003StableTO,
  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},
  year={2003},
  volume={4},
  pages={349-390}
}
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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