Formation and classification of jumps and solitary shock waves in isentropic flows of polytropic continuous media

Conditions for an arbitrary jump occurrence in isentropic flow are studied. It is shown that the jump in gas-dynamic parameters arises as a result of the evolution of a self-similar flow. The concept of self-focusing Riemann waves is introduced. It is shown that an arbitrary jump is formed only by these waves and the conditions for its generation are found. It is shown that there exists a critical velocity, below which a discontinuity cannot be formed isentropically. The second critical value of velocity, exceeding which a discontinuity is formed only in the presence of a vacuum region is found. It is shown that there are only two classes of solitary shock waves: those that form in a medium containing a vacuum region and those that form in a continuous medium. It is shown that not every fall of the Riemann wave leads to the appearance of a shock wave. The results obtained are of a general physical nature, since they are based only on the properties of quasilinear hyperbolic systems.