Analysis of spherically imploding shocks

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Abstract
The self‐similar solution of spherically imploding shock waves is derived analytically for a perfect gas with a constant ratio γ =cp/cv. The basic conservation equations are reduced to a first‐order differential equation in the x‐ y plane. The requirement of a maximum for the pressure curve dictates the values of the self‐similar exponent αm. These values are compared with the previously derived numerical values of αm. When γ=2+√3, the maximum of the pressure occurs at the shock front. The pressure curve then decreases monotonically.