Solitary waves in atomic chains and peridynamical media

Michael Herrmann, Karsten Matthies

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)


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
Issue number2
Publication statusPublished - 7 Mar 2019

Bibliographical note

28 pages, several figures


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


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