The system of equations for one-dimensional unsteady politropic gas motion is considered.
Using Riemann's method the general solution of this system for space periodic initial conditions is obtained.
Exact solutions for politrope power $gamma=3$; $5/3$; $7/5$ are constructed.
For arbitrary politrope power $gamma$ asymptotic solutions are obtained (here small parameter is initial amplitude of perturbation). Formulas for time and space of gradient catastrophe are presented.
Note. Abstracts are published in author's edition
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