Existence and stability of discrete gap breathers in a diatomic beta Fermi-Pasta-Ulam chain

We study the existence and stability of discrete breathers in a chain consisting of alternating light and heavy particles, with nearest-neighbor coupling containing quartic soft or hard anharmonicity. This study is focused on breathers with frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. Simple analytical and physical results obtained through explicit solutions of algebraic equations demonstrate the possibility of the existence of gap breathers with both types of symmetry, i.e., symmetric and antisymmetric. The specific pattern depends on the type of anharmonicity present, i.e., soft or hard, and whether the center of the breather is on a light or a heavy particle. These analytical results are verified systematically through the use of a numerically exact procedure from the anticontinuous limit.