Law of convergence of strong cylindrical and spherical shock waves in a gas with a uniform density

A model of convergence of cylindrical and spherical shock waves in a gas with a uniform density has been considered. The partial differential equations of this model have been reduced to ordinary differential equations, from which the laws of convergence of such shock waves and the dependence $\alpha=f(\gamma, M)$ of their self-similarity index $\alpha$ on the heat capacity ratio $\gamma$ of the gas and their Mach number $M$ have been found. This dependence for cylindrical shock waves in monatomic ($\gamma=1.67$) and diatomic ($\gamma=1.4$) gases has been shown to agree with the experimental data within the measurement error.