37 citations · 168 across the 15 of their papers we have counts for
13 papers · 1 filter
Whitham modulation equations for the regularized Boussinesq equation with cubic nonlinearity
Mark A. Hoefer, Anna Vainchtein
A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Expli…
Solitary waves and kinks in FPU lattices with soft-hard-soft trilinear interactions
Anna Vainchtein, Lev Truskinovsky
We consider a version of the classical Hamiltonian Fermi-Pasta-Ulam (FPU) problem with a trilinear force-strain relation of soft-hard-soft type that is in general non-symmetric. In…
When discrete fronts and pulses form a single family: FPU chain with hardening-softening springs
Anna Vainchtein, Lev Truskinovsky
We consider a version of the classical Hamiltonian FPU (Fermi-Pasta-Ulam) problem with nonlinear force-strain relation in which a hardening response is taken over by a softening re…
Discrete breathers in a mechanical metamaterial
H. Duran, J. Cuevas-Maraver, P. G. Kevrekidis +1
We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges.…
Transition fronts and their universality classes
N. Gorbushin, A. Vainchtein, L. Truskinovsky
Steadily moving transition (switching) fronts, bringing local transformation, symmetry breaking or collapse, are among the most important dynamic coherent structures. The nonlinear…
Stability of traveling waves in a driven Frenkel-Kontorova model
A. Vainchtein, J. Cuevas-Maraver, P. G. Kevrekidis +1
In this work we revisit a classical problem of traveling waves in a damped Frenkel-Kontorova lattice driven by a constant external force. We compute these solutions as fixed points…
Lattices With Internal Resonator Defects
S. Hauver, X. He, D. Mei +5
We consider a variety of settings involving chains with one or more defects stemming from the introduction of nodes bearing internal resonators. Motivated by experimental results i…
An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices
Haitao Xu, Jesús Cuevas--Maraver, Panayotis G. Kevrekidis +1
In this work, we revisit a criterion, originally proposed in [Nonlinearity {\bf 17}, 207 (2004)], for the stability of solitary traveling waves in Hamiltonian, infinite-dimensional…
A Unifying Perspective: Solitary Traveling Waves As Discrete Breathers And Energy Criteria For Their Stability
J. Cuevas-Maraver, P. G. Kevrekidis, A. Vainchtein +1
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pas…
Breathers in a locally resonant granular chain with precompression
Lifeng Liu, Guillaume James, Panayotis Kevrekidis +1
We study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective n…
Nonlinear waves in a strongly nonlinear resonant granular chain
Lifeng Liu, Guillaume James, Panayotis Kevrekidis +1
We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system,…
Traveling Wave Solutions in a Chain of periodically Forced Couple Nonlinear Oscillators
Mei Duanmu, Nathaniel Whitaker, Panos Kevrekidis +2
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillato…
Interaction of Traveling Waves with Mass-With-Mass Defects within a Hertzian Chain
P. G. Kevrekidis, A. Vainchtein, M. Serra Garcia +1
We study the dynamic response of a granular chain of particles with a resonant inclusion (i.e., a particle attached to a harmonic oscillator, or a mass-with-mass defect). We focus…