Discrete breathers with hard and soft type of nonlinearity in 1D Morse lattices with long-range interactions

Recently the focus of studies on discrete breathers has arguably shifted from the mathematical proof of their existence in simplified nonlinear lattices towards the search for the long-lived quasi-breathers in real systems, e.g., in crystal lattices. In each particular field, different factors should be taken into account. Atoms in crystals typically interact not only with the nearest neighbors and thus, the effect of long-range interatomic forces is an important issue. When the long-range forces are involved, the tails of the interatomic potentials contribute essentially to the dynamics of the system and in these circumstances one cannot use truncated Taylor expansions of the potentials such as cubic or quartic. In this work we discuss various discrete breathers (more precisely, quasi-breathers) that can be excited in 1D monatomic and diatomic Morse lattices with long-range interactions and sinusoidal on-site potential. This model describes at a qualitative level discrete breathers in pure metals and ordered alloys.