Solitary waves in atomic chains and peridynamical media

TL;DR

This paper establishes the existence of solitary traveling waves in nonlocal Hamiltonian systems modeled by peridynamics, extending lattice models, and explores their numerical computation and asymptotic behaviors.

Contribution

It proves the existence of solitary waves in peridynamical media with super-quadratic potentials using a variational approach, and analyzes their numerical and asymptotic properties.

Findings

Existence of solitary traveling waves proven for super-quadratic potentials.

Numerical methods for computing these waves are discussed.

Asymptotic regimes of the waves are studied.

Abstract

Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of solitary traveling waves for super-quadratic potentials by maximizing the potential energy subject to both a norm and a shape constraint. We also discuss the numerical computation of waves and study several asymptotic regimes.