Absolute and convective instabilities of waves on unbounded and large bounded domains

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Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit (2005, background): “1) stems from spatial dynamics, for complex conjugate leading eigenvalues the absolute spectrum (see [32] is unstable, which typically”
Computing absolute and essential spectra using continuation (2007, background): “In [13], we showed that the stability of coherent structures in such large but finite domains can be characterized using spectral information on the unbounded domain together with information on localized boundary modes: As the size of the domain goes to infinity, spectra in large domains converge t”
On the Structure of Spectra of Modulated Travelling Waves (2001, unknown): “A second related issue is to determine the existence and stability of other modulated waves that are related to the primary wave.”
On the Stability of Periodic Travelling Waves with Large Spatial Period (2001, background): “The fate of the essential spectrum under truncation to periodic (and other) boundary conditions has recently been determined in [39].”