Optical-acoustical interaction in FPU-chains with alternating large masses (plus appendix)

One of the problems of periodic FPU-chains with alternating masses is whether significant interactions exist between the so-called (high frequency) optical and (low frequency) acoustical groups. We show that for $\alpha$-chains with $4n$ and $8n$ particles ($n= 1, 2, \ldots$) we have significant interactions caused by external forcing. For $\beta$-chains with $4$ and $8$ particles the interactions are characterised by parametric forcing, the interactions are negligible.