24 citations · 72 across the 28 of their papers we have counts for
11 papers · 1 filter
Radiating Solitary Waves in an FPUT Lattice with Random Coefficients
Hermen Jan Hupkes, Joshua A. McGinnis, Rik W. S. Westdorp +1
We study the propagation of solitary waves in a Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with small random heterogeneity in the linear spring force. Perturbed by the random environm…
Small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou lattices
Timothy E. Faver, Hermen Jan Hupkes, J. Douglas Wright
We prove the existence of small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices without assumptions of physical symmetry. Such lattices are inf…
Propagation reversal for bistable differential equations on trees
Hermen Jan Hupkes, Mia Jukić, Petr Stehlík +1
We study traveling wave solutions to bistable differential equations on infinite -ary trees. These graphs generalize the notion of classical square infinite lattices and our res…
Curvature-driven front propagation through planar lattices in oblique directions
Mia Jukić, Hermen Jan Hupkes
In this paper we investigate the long-term behaviour of solutions to the discrete Allen-Cahn equation posed on a two-dimensional lattice. We show that front-like initial conditions…
Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions
Willem M. Schouten-Straatman, Hermen Jan Hupkes
We investigate the impact of spatial-temporal discretisation schemes on the dynamics of a class of reaction-diffusion equations that includes the FitzHugh-Nagumo system. For the te…
Exponential Dichotomies for Nonlocal Differential Operators with Infinite Range Interactions
Willem M. Schouten-Straatman, Hermen Jan Hupkes
We show that MFDEs with infinite range discrete and/or continuous interactions admit exponential dichotomies, building on the Fredholm theory developed by Faye and Scheel for such…
Dynamics of curved travelling fronts for the discrete Allen-Cahn equation on a two-dimensional lattice
Mia Jukić, Hermen Jan Hupkes
In this paper we consider the discrete Allen-Cahn equation posed on a two-dimensional rectangular lattice. We analyze the large-time behaviour of solutions that start as bounded pe…
Counting and ordering periodic stationary solutions of lattice Nagumo equations
Hermen Jan Hupkes, Leonardo Morelli, Petr Stehlík +1
We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs…
Multichromatic travelling waves for lattice Nagumo equations
Hermen Jan Hupkes, Leonardo Morelli, Petr Stehlík +1
We discuss multichromatic front solutions to the bistable Nagumo lattice differential equation. Such fronts connect the stable spatially homogeneous equilibria with spatially heter…
Travelling waves for spatially discrete systems of FitzHugh-Nagumo type with periodic coefficients
W. M. Schouten, H. J. Hupkes
We establish the existence and nonlinear stability of travelling wave solutions for a class of lattice differential equations (LDEs) that includes the discrete FitzHugh-Nagumo syst…
Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions
W. M. Schouten, H. J. Hupkes
We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum l…