General solutions of the equations of one-dimensional gas motion were obtained for the special cases where the exponent is ? = 5/3, 7/5. For these cases the periodical space variable solutions were constructed. The dependences of the time of the gradient catastrophe on the initial wave amplitude were obtained. A review of the results obtained by the author on the general properties of the basic equations describing the motion of quasi-gas media is presented in the article. The condition of periodicity of solutions of these equations for the space variable was obtained. The analogy with the system of equations for one-dimensional gas dynamics was suggested. For special types of quasi-gas media the exact periodic space variable solutions were constructed and examined.
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