Centred compression-wave in polytropic gas, and its disintegration

The isentropic plane motion of a loaded half-space filled with a polytropic gas is examined. The problem of the one-dimensional motion is formulated assuming that the laws of conservation of mass and momentum are obeyed. A solution is given for the case of a centered cumulation of a straight wave of finite deformation. The isentropic and shock adiabatic properties are discussed and the wave-front configuration after cumulation of the compression wave is analyzed. It is shown that for the polytropic exponent less than or equal to 5/3, disintegration of arbitrary discontinuity generated by the centered compression wave in the polytropic gas can result in the formation of a single shock wave, followed by a contact discontinuity behind which a rarefaction wave moves.