Existence of solitary waves in one dimensional peridynamics

TL;DR

This paper rigorously proves the existence of solitary waves in a one-dimensional peridynamics model by adapting a variational approach originally developed for lattice equations, addressing short-range interactions.

Contribution

It introduces a novel adaptation of the variational framework to establish solitary wave existence in peridynamics, extending prior methods to this continuum model.

Findings

Existence of solitary waves in 1D peridynamics confirmed.

Method adapts lattice variational techniques to continuum models.

Addresses challenges of short-range interaction truncation.

Abstract

We give a rigorous proof of existence for solitary waves of a peridynamics model in one space dimension recently investigated by Silling (J. Mech. Phys. Solids 96:121--132, 2016). We adapt the variational framework developed by Friesecke and Wattis (Comm. Math Phys. 161:391--418, 1994) for the Fermi-Pasta-Ulam-Tsingou lattice equations to treat a truncated problem which cuts off short-range interactions, then pass to the limit.