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Solitary waves in atomic chains and peridynamical media

1 Technische Universität Braunschweig, Institute of Computational Mathematics, Universitätsplatz 2, 38106 Braunschweig, Germany
2 University of Bath, Department of Mathematical Sciences, Bath, BA2 7AY, United Kingdom
$^\dagger$ This contribution is part of the Special Issue: Hamiltonian Lattice Dynamics
Guest Editors: Simone Paleari; Tiziano Penati

Special Issues: Hamiltonian Lattice Dynamics

## Abstract    Full Text(HTML)    Figure/Table    Related pages

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.
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