Breathers on a diatomic FPU chain

Abstract

Existence of self-localized time-periodic vibrations (discrete breathers) is proved for alternating mass chains with anharmonic coupling and no external potential, provided the mass ratio is large enough. This result is significant because, except for special cases, previous proofs of existence of discrete breathers require the phonon spectrum to be a narrow band bounded away from zero (optic phonons), whereas this problem has also an acoustic band (frequencies arbitrarily close to zero). The method can be adapted to many other cases with both acoustic and optic phonons.