14 citations · 27 across the 10 of their papers we have counts for
9 papers · 1 filter
Phase-Shifted Nanopteron Solutions to a Singularly Perturbed Korteweg--de Vries Equation
Timothy E. Faver
We construct nanopteron solutions to the differential equation \[ ε^2u^{(4)}+u''-u+u^2 =0, \] which is a singular perturbation of the traveling wave problem for the K…
Mass and spring dimer Fermi-Pasta-Ulam-Tsingou nanopterons with exponentially small, nonvanishing ripples
Timothy E. Faver, Hermen Jan Hupkes
We study traveling waves in mass and spring dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices in the long wave limit. Such lattices are known to possess nanopteron traveling waves in…
Scaling Relations for Auxin Waves
Timothy E. Faver, Hermen Jan Hupkes, Roeland M. H. Merks +1
We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show…
Micropterons, Nanopterons and Solitary Wave Solutions to the Diatomic Fermi-Pasta-Ulam-Tsingou Problem
Timothy E. Faver, Hermen Jan Hupkes
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…
Solitary Waves in Mass-in-Mass Lattices
Timothy E. Faver, Roy H. Goodman, J. Douglas Wright
We consider the existence of spatially localized traveling wave solutions of the mass-in-mass lattice. Under an anti-resonance condition first discovered by Kevrekidis, Stefanov an…
Small mass nanopteron traveling waves in mass-in-mass lattices with cubic FPUT potential
Timothy E. Faver
The mass-in-mass (MiM) lattice consists of an infinite chain of identical beads that are both nonlinearly coupled to their nearest neighbors and linearly coupled to a distinct reso…
Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit
Timothy E. Faver, Hermen Jan Hupkes
The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain of alternating particles connected by identical nonlinear springs. We prove the existence of micropteron t…
Nanopteron-stegoton traveling waves in spring dimer Fermi-Pasta-Ulam-Tsingou lattices
Timothy E. Faver
We study the existence of traveling waves in a spring dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. This is a one-dimensional lattice of identical particles connected by alternati…
Exact diatomic Fermi-Pasta-Ulam-Tsingou solitary waves with optical band ripples at infinity
Timothy E. Faver, J. Douglas Wright
We study the existence of solitary waves in a diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. For monatomic FPUT the traveling wave equations are a regular perturbation of the Ko…