Stability of Discrete Breathers in Diatomic Fermi-Pasta-Ulam Type Lattices

We consider the 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. Existence of the discrete breathers is proved for small mass ratio by continuation from the anti-continuous limit. We prove that the discrete breather is linearly stable if it is continued from a solution consisting of alternating anti-phase excited particles, otherwise it is linearly unstable, near the anti-continuous limit.