2020/05/24 by Carter, Paul, Rademacher, Jens D. M., Sandstede, Björn
#34E17 #35B25 #35B35 #35C07 #35P15 #37L15 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.2005.11683
Motivated by pulse-replication phenomena observed in the FitzHugh--Nagumo equation, we investigate traveling pulses whose slow-fast profiles exhibit canard-like transitions. We show that the spectra of the PDE linearization about such pulses may contain many point eigenvalues that accumulate onto a union of curves as the slow scale parameter approaches zero. The limit sets are related to the absolute spectrum of the homogeneous rest states involved in the canard-like transitions. Our results are formulated for general systems that admit an appropriate slow-fast structure.