Solitary waves in atomic chains and peridynamical media

• Main Authors: Michael Herrmann, Karsten Matthies
• Format: Article
• Language: English
• Published: AIMS Press 2019-09-01
• Series: Mathematics in Engineering
• Subjects: peridynamics; Hamiltonian lattices; solitary waves; variational; asymptotic analysis
• Online Access: https://www.aimspress.com/article/10.3934/mine.2019.2.281/fulltext.html
• ISSN: 2640-3501

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.