Solitary waves in atomic chains and peridynamical media

Michael Herrmann, Karsten Matthies

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)281-308
Number of pages28
JournalMathematics in Engineering
Volume1
Issue number2
DOIs
Publication statusPublished - 7 Mar 2019

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norms
traveling waves
differential equations
solitary waves
potential energy
interactions

Keywords

  • math.NA
  • math.DS
  • 37K40, 37K60, 47J30, 74J30, 74H15

Cite this

Solitary waves in atomic chains and peridynamical media. / Herrmann, Michael; Matthies, Karsten.

In: Mathematics in Engineering, Vol. 1, No. 2, 07.03.2019, p. 281-308.

Research output: Contribution to journalArticle

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