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Solitary waves in mass-in-mass lattices

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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.

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Acknowledgements

The discussion of the \(\mu \rightarrow \infty \) limit was suggested by a referee and is, in fact almost identical, in content and language, to the referee report. We thank them for this contribution.

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Authors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Timothy E. Faver

  2. New Jersey Institute of Technology, Newark, USA

    Roy H. Goodman

  3. Drexel University, Philadelphia, USA

    J. Douglas Wright

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  1. Timothy E. Faver
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Correspondence to J. Douglas Wright.

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Faver, T.E., Goodman, R.H. & Wright, J.D. Solitary waves in mass-in-mass lattices. Z. Angew. Math. Phys. 71, 197 (2020). https://doi.org/10.1007/s00033-020-01384-8

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

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