Existence and stability of discrete breathers in diatomic Fermi–Pasta–Ulam type lattices

Abstract

We consider discrete breathers in one-dimensional diatomic Fermi–Pasta–Ulam type lattices. A discrete breather in the limit of zero mass ratio, i.e. the anti-continuous limit, consists of a finite number of in-phase or anti-phase excited light particles, separated by particles at rest. The existence of discrete breathers is proved for small mass ratio by continuation from the anti-continuous limit. We prove that the discrete breathers are all unstable near the anti-continuous limit, except for those continued from solutions consisting of alternating anti-phase excited particles.