8 papers
Weak and strong interaction of excitation kinks in scalar parabolic equations
Antoine Pauthier, Jens D. M. Rademacher, Dennis Ulbrich
Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest…
Domain wall motion in axially symmetric spintronic nanowires
Jens D. M. Rademacher, Lars Siemer
This article is concerned with the dynamics of magnetic domain walls (DWs) in nanowires as solutions to the classical Landau-Lifschitz-Gilbert equation augmented by a typically non…
Pulse replication and accumulation of eigenvalues
Paul Carter, Jens D. M. Rademacher, Björn Sandstede
Motivated by pulse-replication phenomena observed in the FitzHugh--Nagumo equation, we investigate traveling pulses whose slow-fast profiles exhibit canard-like transitions. We sho…
The impact of advection on the stability of stripes on lattices near planar Turing instabilities
Jichen Yang, Jens D. M. Rademacher, Eric Siero
Striped patterns are known to bifurcate in reaction-diffusion systems with differential isotropic diffusions at a supercritical Turing instability. In this paper we study the impac…
The impact of advection on large-wavelength stability of stripes near planar Turing instabilities
Jichen Yang, Jens D. M. Rademacher, Eric Siero
It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of wea…
Inhomogeneous domain walls in spintronic nanowires
Lars Siemer, Ivan Ovsyannikov, Jens D. M. Rademacher
In case of a spin-polarized current, the magnetization dynamics in nanowires are governed by the classical Landau-Lifschitz equation with Gilbert damping term, augmented by a typic…