The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas dynamics equations can be rewritten in a variational form. Such a Lagrangian is found in the paper. Complete group analysis of the Euler–Lagrange equation is performed. The found Lagrangian and the symmetries are used to derive conservation laws in Lagrangian variables by means of Noether’s theorem. The analogs of the newly found conservation laws in Eulerian coordinates are presented as well.

中文翻译：

---

拉格朗日坐标中相对论气体动力学一维方程的守恒律

本文着重分析一维相对论气体动力学方程。在拉格朗日描述中考虑了所研究的方程，从而有可能找到拉格朗日，使得相对论气体动力学方程可以以变分形式重写。在本文中发现了这样的拉格朗日式。进行了欧拉-拉格朗日方程的完整群分析。借助Noether定理，将找到的Lagrangian和对称性用于得出Lagrangian变量中的守恒律。还介绍了欧拉坐标中新发现的守恒定律的类似物。