We examine nonlinear lattice excitations in a model for a solid which may undergo a displacive structural phase transition. In particular, we investigate the field equations for a diatomic chain of atoms including nonlinear potentials on one species. We identify three classes of excitations in this model. These are linearized phonons, large amplitude solitary waves, and nonlinear phonons. Interactions between the linear phonons and the nonlinear modes give rise to a translation mode which is a further solution of the field equations. The linear and nonlinear phonons are also direct solutions of the discrete equations of motion. However, using the molecular dynamics technique we find that kink-type configurations occur for a much larger parameter space in the discrete lattice than they do in the continuum description. All the stable excitations of the field equations should be included in a formal description (e.g. statistical mechanics) of the model.
Vector Spatiotemporal Solitons in cold atomic gases with linear and nonlinear PT symmetric potentials
