Solitary Waves in Mass-in-Mass Lattices

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...

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Bibliographic Details
Published in:arXiv.org 2020-02
Main Authors: Faver, Timothy E, Goodman, Roy H, Wright, J Douglas
Format: Article
Language:English
Subjects:
Computer simulation
Lattices (mathematics)
Solitary waves
Traveling waves
Online Access:Get full text
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Summary: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 weakly unstable
ISSN:2331-8422
DOI:10.48550/arxiv.2002.05573