Waves in a gradient-elastic medium with surface energy

The propagation of different types of elastic waves in a gradient-elastic medium with surface energy is considered. The dispersion characteristics of longitudinal and shear body waves, Rayleigh surface waves and antiplane shear surface waves, and antiplane shear waves in a layer are analysed in a linear approximation. Antiplane shear surface waves are also investigated taking geometrical non-linearity into account; their modulation instability, which leads to self-modulation and the formation of stationary envelope waves is also considered.