Solitary waves in mass-in-mass lattices

Document Type

Article

Publication Date

12-1-2020

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.

Identifier

85095118623 (Scopus)

Publication Title

Zeitschrift Fur Angewandte Mathematik Und Physik

External Full Text Location

https://doi.org/10.1007/s00033-020-01384-8

ISSN

00442275

Issue

6

Volume

71

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