On the various methods of adaptation of frontline ray expansions scheme in the problems of the axisymmetric dynamics of nonlinear elastic medium

The possibility of using of two variants of the ray method modification is shown on the example of several one-dimensional axisymmetric problems of shock deformation of elastic medium. The ray method in its standard can not be applied to nonlinear processes, including discontinuities surfaces of the first derivatives. Presented in the paper variants of the method allow to remove this restriction. Features of the application of the ray series for distribution in the medium of a single shock wave, for the process leading to the formation of several shock waves of various types, for the problem of formation of reflected waves and their subsequent interaction with the leading edges of initially created processes are shown. The question of construction of ray series for times after the interaction of the incident and reflected shock waves in the interior layer of the elastic medium is considered.