Propagation reversal on trees in the large diffusion regime

In this work we study travelling wave solutions to bistable reaction diffusion equations on bi-infinite $k$-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by Bates and his coworkers, we find an asymptotic prediction for the speed of travelling front solutions. In addition, we prove that the associated profiles converge to the solutions of a suitable limiting reaction-diffusion PDE. Finally, for the standard cubic nonlinearity we provide explicit formula's to bound the thin region in parameter space where the propagation direction undergoes a reversal

Micropterons, Nanopterons and Solitary Wave Solutions to the Diatomic Fermi-Pasta-Ulam-Tsingou Problem

We use a specialized boundary-value problem solver for mixed-type functional differential equations to numerically examine the landscape of traveling wave solutions to the diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) problem. By using a continuation approach, we are able to uncover the relationship between the branches of micropterons and nanopterons that have been rigorously constructed recently in various limiting regimes. We show that the associated surfaces are connected together in a nontrivial fashion and illustrate the key role that solitary waves play in the branch points. Finally, we numerically show that the diatomic solitary waves are stable under the full dynamics of the FPUT system