Instability of solitary waves in non-linear composite media

The problem is considered about dynamic instability of soliton solutions (solitary waves) of Hamilton equations describing plane waves in nonlinear elastic composite media in the presence and absence of anisotropy. In the anisotropic case, two two-parametric families of solitary waves (fast and slow ones) exist, and one three-parametric family exists in the anisotropy absence. The main equations are given that describe plane waves in nonlinear anisotropic elastic composites.