Periodic Traveling Waves in Diatomic Granular Chains

We study bifurcations of periodic traveling waves in diatomic granular chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter, and the periodic waves with a 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, where periodic traveling waves of homogeneous granular chains exist.