49 citations · 253 across the 59 of their papers we have counts for
4 papers · 1 filter
Fronts in the wake of a parameter ramp: slow passage through pitchfork and fold bifurcations
Ryan Goh, Tasso J. Kaper, Arnd Scheel +1
This work studies front formation in the Allen-Cahn equation with a parameter heterogeneity which slowly varies in space. In particular, we consider a heterogeneity which mediates…
Pushed-to-pulled front transitions: continuation, speed scalings, and hidden monotonicity
Montie Avery, Matt Holzer, Arnd Scheel
We analyze the transition between pulled and pushed fronts both analytically and numerically from a model-independent perspective. Based on minimal conceptual assumptions, we show…
Coherent structures in nonlocal systems -- functional analytic tools
Olivia Cannon, Arnd Scheel
We develop tools for the analysis of fronts, pulses, and wave trains in spatially extended systems with nonlocal coupling. We first determine Fredholm properties of linear operator…
Nonlinear eigenvalue methods for linear pointwise stability of nonlinear waves
Arnd Scheel
We propose an iterative method to find pointwise growth exponential growth rates in linear problems posed on essentially one-dimensional domains. Such pointwise growth rates captur…