ABSTRACT
This chapter presents a comprehensive overview of investigations devoted to the atomistic simulations of nonlinear excitations in two-dimensional (2-D) materials with an emphasis on graphene and its derivatives. The role of interatomic potentials in molecular dynamics studies of nonlinear effects is discussed. A detailed analysis of the dynamics of one- and two-component delocalized vibrational modes is given, and their possible effect on the mechanical properties of graphene is presented. The interrelation between spatially localized and delocalized vibrational modes is discussed, and new types of localized vibrational states, also called discrete breathers (DBs), obtained for graphene as a result of this analysis are presented. Other recent achievements in the study of nonlinear lattice dynamics of 2-D materials are presented, and open problems are listed.
