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Solitary waves in atomic chains and peridynamical media

  • Received: 23 September 2018 Accepted: 23 January 2019 Published: 07 March 2019
  • Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-di erential 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.

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

    Related Papers:

  • Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-di erential 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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