Solitary waves in atomic chains and peridynamical media
Numerical Analysis
2019-04-24 v2 Dynamical Systems
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.
Cite
@article{arxiv.1810.01476,
title = {Solitary waves in atomic chains and peridynamical media},
author = {Michael Herrmann and Karsten Matthies},
journal= {arXiv preprint arXiv:1810.01476},
year = {2019}
}
Comments
revised version with corrected typos and minor changes; 25 pages, several figures