10 papers
Dissipative bright and dark pulses under periodic forcing
Lukas Bengel, Björn de Rijk
We analyze the existence and stability of bright and dark pulses in a damped nonlinear Schrödinger (NLS) equation with periodic forcing. This Lugiato-Lefever equation is a canonica…
Nonlinear stability of periodic waves in the Korteweg-de Vries equation under localized perturbations
Emile Bukieda, Björn de Rijk
We investigate the stability and asymptotic behavior of spatially periodic cnoidal waves in the Korteweg-de Vries equation subject to localized perturbations. Standard stability ar…
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 of coherent pattern formation through invasion in the FitzHugh-Nagumo system
Montie Avery, Paul Carter, Björn de Rijk +1
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are cri…
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…
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…