Abstract The theory of construction of exact analytical solutions of the Cauchy problem using the power series depending on a special time variable whose form determines the particular class of motion is developed within one-dimensional time-dependent gas dynamics. Generally, the recurrent relations to the coefficients are finite and arranged so that there is no need to solve differential equations or integrate for calculation of the unknown functions and all the terms of series are determined successively from the initial conditions using only the algebraic operations and differentiation. This fact makes it possible also to find the terms of series exactly using any mathematical software package which admits of symbolic transformations. The necessary boundary conditions are discussed and the control techniques for the behavior of series are outlined. Some examples of the physical problems solved with the use of the method proposed are examined.

中文翻译：

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气体动力学方程的精确解析解

摘要 使用依赖于特定时间变量的幂级数构建柯西问题精确解析解的理论是在一维时间相关的气体动力学中发展起来的。通常，系数的循环关系是有限的，并且排列成不需要求解微分方程或积分来计算未知函数，并且所有级数项仅使用代数运算和微分从初始条件连续确定. 这一事实使得也可以使用任何允许符号变换的数学软件包来精确地找到级数的项。讨论了必要的边界条件，并概述了系列行为的控制技术。检查了使用所提出的方法解决的物理问题的一些示例。