Discrete Breathers and Discrete Oscillating Kink Solution in the Mass-in-mass Chain in the State of Acoustic Vacuum

The present study is concerned with the dynamics of special localized solutions emerging in the mass-in-mass anharmonic oscillatory chain in the state of acoustic vacuum. Each outer element of the chain incorporates an additional, purely nonlinear mass attachment. Using the homogeneity of the system under consideration, we use the separation of time and space and reduce the analysis of standing wave solutions supported by the chain to the analysis of an algebraic system. An analytical study of the latter revealed the distinct types of static discrete breather solutions as well as the discrete oscillating kinks. Along with the analytical description of their spatial wave profiles, we also establish their zones of existence in the space of system parameters. The stability properties of these solutions are assessed through the linear stability analysis (Floquet). All analytical models are supported by the numerical simulations of the full model.