Formation of strain solitary waves in the Cosserat continuum with restricted rotation

The nonlinear viscoelastic micropolar medium with restricted rotation (the Cosserat pseudo-continuum) is considered. Using the method of coupled normal waves, the original nonlinear system describing the dynamics of the medium is transferred to a system of evolutionary equations. It is shown that these evolutionary equations are four nonlinear partial differential equations two of which are the Burgers equations and the other two are the modified Korteweg-de Vries (mKdV) equations. The paper presents the results of the analytical and numerical study of nonlinear viscoelastic wave evolution.