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M. Betti and D.E. Pelinovsky

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Periodic Travelling Waves in Dimer Granular Chains

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Journal of Nonlinear Science 23, 689-711 (2013)

**Abstract:**

We study bifurcations of periodic travelling waves in granular dimer chains from the anticontinuum
limit, when the mass ratio between the light and heavy beads is zero. We show that
each limiting periodic wave is uniquely continued with respect to the mass ratio parameter
and the periodic waves with the wavelength larger than a certain critical value are spectrally
stable. Numerical computations are developed to study how this solution family is continued
to the limit of equal mass ratio between the beads.

**Keywords:**

Fermi-Pasta-Ulam lattice, traveling periodic waves, anti-continuum limit,
existence and stability, Floquet multipliers, Krein signature.