Evolution of Pulse and Periodic Elastic Waves in Media with Quadratically-Bimodular Nonlinearity

On the basis of the elastic contact model of rough surfaces of solids, a quadraticallybimodular equation of state for micro-inhomogeneous media containing cracks is derived. A study is made of the propagation of elastic single unipolar pulse perturbations and bipolar periodic waves in such media. Exact analytical solutions that describe the evolution of initially triangular pulses and periodic sawtooth waves are obtained. A numerical and graphical analysis of the solutions is also carried out.