8 papers · 1 filter
Selection of pushed pattern-forming fronts in the FitzHugh-Nagumo system
Montie Avery, Paul Carter, Björn de Rijk
We establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, f…
Stability and dynamics of planar fronts in reaction-diffusion systems under nonlocalized perturbations
Björn de Rijk, Joris van Winden
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on . Under standard spectral stability assumptions, we…
Diffusive synchronization of phase waves in the FitzHugh-Nagumo system
Montie Avery, Paul Carter, Björn de Rijk +1
We analyze synchronization of relaxation oscillations in multiple-timescale reaction-diffusion systems. Interpreting synchronization as convergence to frequency-synchronized wave-t…
Global existence and decay of small solutions in a viscous half Klein-Gordon equation
Louis Garénaux, Björn de Rijk
We establish global existence and decay of solutions of a viscous half Klein-Gordon equation with a quadratic nonlinearity considering initial data, whose Fourier transform is smal…
Orbital stability of plane waves in the Klein-Gordon equation against localized perturbations
Emile Bukieda, Louis Garénaux, Björn de Rijk
We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render…
Existence and stability of soliton-based frequency combs in the Lugiato-Lefever equation
Lukas Bengel, Björn de Rijk
Kerr frequency combs are optical signals consisting of a multitude of equally spaced excited modes in frequency space. They are generated by converting a continuous-wave pump laser…