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.

本研究涉及声真空状态下质量中质量非谐振荡链中出现的特殊局部解的动力学。链条的每个外部元件都包含一个额外的、纯非线性的质量附件。利用所考虑的系统的同质性，我们使用时间和空间的分离，并将链支持的驻波解的分析简化为代数系统的分析。对后者的分析研究揭示了不同类型的静态离散呼吸器解决方案以及离散振荡扭结。随着对它们的空间波剖面的分析描述，我们还在系统参数空间中建立了它们的存在区域。这些溶液的稳定性特性通过线性稳定性分析 (Floquet) 进行评估。所有分析模型都得到完整模型的数值模拟的支持。