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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
  Link: http://www.aimspress.com/newsinfo/1165.html

Special Issues: Hamiltonian Lattice Dynamics

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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Keywords peridynamics; Hamiltonian lattices; solitary waves; variational; asymptotic analysis

Citation: Michael Herrmann, Karsten Matthies. Solitary waves in atomic chains and peridynamical media. Mathematics in Engineering, 2019, 1(2): 281-308. doi: 10.3934/mine.2019.2.281

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