High-low frequency interaction in alternating FPU alfa-chains

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One of the problems of periodic FPU-chains with alternating large masses is whether signifi- cant interactions exist between the so-called (high frequency) optical and (low frequency) acoustic groups. We show that for ↵-chains with 2n particles we have significant interactions caused by external forcing of the acoustic modes by a stable or unstable optical normal mode. In the proofs an embedding theorem plays a part; the analysis is straightforward in the case that n is even, a di↵erent approach using invariant manifolds with symmetry is needed if n is odd. For -chains the interactions are characterised by parametric excitation, there are indications that interaction is negligible.
Original languageEnglish
Article number103686
Pages (from-to)1-9
Number of pages9
JournalInternational Journal of Non-Linear Mechanics
Publication statusPublished - May 2021


  • Fermi–Pasta–Ulam chain
  • Alternating mass
  • High–low frequency interaction
  • Invariant manifolds
  • Symmetry


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