Dynamics and Numerical Analysis of Intrinsic Localized Mode in Crystals

Nonlinear lattice models have been extensively investigated to understand the fundamental properties of vibrations and wave propagation in crystal structures. Recently, intrinsic localized modes (ILMs), also known as discrete breathers (DBs), have attracted considerable interest due to their unique properties and applications in various engineering fields. In this paper, we present the concept and fundamental properties of ILMs within the framework of theoretical lattice models. Since crystal structures can be interpreted as nonlinear lattice systems, they inherently support the existence of ILMs. We also discuss recent advancements in the study of ILMs as atomic vibrations in crystals, highlighting several significant findings. Furthermore, we introduce a numerical method for obtaining solutions of moving ILMs and analyze their dynamics through molecular dynamics simulations. Additionally, we explore energy transport mechanisms facilitated by nonlinear waves and vibrations, such as nonlinear phonons and ILMs.