Solitary waves in mass-in-mass lattices

Timothy E. Faver, Roy H. Goodman, J. Douglas Wright

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the existence of spatially localized traveling wave solutions of the mass-in-mass lattice. Under an anti-resonance condition first discovered by Kevrekidis, Stefanov and Xu, we prove that such solutions exist in two distinguished limits; the first where the mass of the internal resonator is small and the second where the internal spring is very stiff. We then numerically simulate the solutions, and these simulations indicate that the anti-resonant traveling waves are very weakly unstable.

Original languageEnglish (US)
Article number197
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume71
Issue number6
DOIs
StatePublished - Dec 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

Keywords

  • Fermi Pasta Ulam Tsingou Lattice
  • Lattice differential equations
  • Mass-in-mass lattices
  • Solitary waves

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