Negative group velocity in solids

Waves with the negative group velocity (NGV) are known to exist in optics (Sommerfeld and Brillouin) and in some mechanical cases like layered media, cylindrical shells and cylinders. In this paper the effects of the NGV on the evolution of the wave profiles are studied in the context of a Mindlin type continuum model with two microstructures in the 1D setting. Based on dispersion analysis, the range of parameters when the NGV region exists is determined. Numerical analysis is used to establish effects of the NGV in the evolution of wave profiles in time. The results can be used in material science.