40 citations · 128 across the 11 of their papers we have counts for
12 papers
Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio
Aaron Hoffman, J. Douglas Wright
Consider an infinite chain of masses, each connected to its nearest neighbors by a (nonlinear) spring. This is a Fermi-Pasta-Ulam-Tsingou lattice. We prove the existence of traveli…
Invasion fronts on graphs: the Fisher-KPP equation on homogeneous trees and Erdős-Réyni graphs
Aaron Hoffman, Matt Holzer
We study the dynamics of the Fisher-KPP equation on the infinite homogeneous tree and Erdős-Réyni random graphs. We assume initial data that is zero everywhere except at a single n…
Characterizing Traveling Wave Collisions in Granular Chains Starting from Integrable Limits: the case of the KdV and the Toda Lattice
Y. Shen, P. G. Kevrekidis, S. Sen +1
Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To tha…
Entire Solutions for Bistable Lattice Differential Equations with Obstacles
A. Hoffman, H. J. Hupkes, E. Van Vleck
We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obs…
Orbital Stability of Localized Structures via Backlund Transformations
A. Hoffman, C. E. Wayne
The Backlund Transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite dimensio…
Multidimensional Stability of Waves Travelling Through Rectangular Lattices in Rational Directions
A. Hoffman, H. J. Hupkes, E. Van Vleck
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagat…