The evolutionary equation for one-dimensional shear waves of a rupture of strains

The problem about formation and the subsequent distribution of the one-dimensional shear shock wave in nonlinear elastic incompressible isotropic half-space is solved. Application of a method of the spliced asymptotic expansions in front field of a shock wave leads to the evolutionary quasilinear wave equation which is distinct from the equations of Hopf, characteristic for volume shock waves. Some methods of build-up of solutions for the evolutionary equations of the shift waves, allowing to consider the manifold time functions in the capacity of boundary conditions for a field of transitions, are offered.