Solitary waves in nonlinear microstructured materials

Dispersive effects due to microstructure of materials combined with nonlinearities give rise to solitary waves. In this paper the existence of solitary wave solutions is proved for a rather general hierarchical governing equation which accounts for nonlinearities on both macro- and microscales. Properties of the waves are established. Waves are asymmetric in the case of the nonlinearity in the microscale. Dispersive effects are due to the scale dependence.