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This paper presents the dynamic model of the soliton. Based on this model, it is supposed to study the state of the shock wave and the transition of the wave to another state. The theory and experiment of cylindrical shock waves is presented in the literature. Shock waves in low-temperature plasma are of interest both from scientific and applied fields. The shock wave causes a rapid increase in temperature and pressure in the discharge area. The release of energy in the discharge before the shock wave front affects its speed and other characteristics. In the experiment, it was found that the wave front has two stages in the structure. A second reflected wave is observed inside the cylinder. In this experiment, the secondary wave is formed at smaller distances from the edge of the cylinder, in the absence of a discharge, the absence of a second front.