On Two-Dimensional Longitudinal Nonlinear Waves in Graphene Lattice

A two-dimensional graphene lattice model with translational and angular interactions between the elements of two sublattices is considered. The nonlinearity is introduced via nonlinearly elastic translational forces between the masses in the lattice. The nonlinear strain behaviour is studied using the continuum limit of the lattice that results in the derivation of four coupled governing equations describing the dynamics of interacting sublattices. An asymptotic procedure is developed to account for weakly transversely perturbed nonlinear longitudinal plane waves giving rise to a two-dimensional nonlinear governing equation for longitudinal strains.