Abstract

A special subclass of solutions of the three-dimensional system of ideal polytropic gas equations corresponding to an atmospheric model is considered. The properties of these solutions are completely characterized by a high-order nonlinear system of ordinary differential equations. Unlike the corresponding two-dimensional model, all singular points of this system have been found to be unstable. Some first integrals of this system have been found. In the case of axial symmetry, the system can be reduced to a single equation. If the adiabatic exponent is equal to 2, the system is integrable.

中文翻译：

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简化大气模型方程的一个子类解

摘要

考虑了对应于大气模型的理想多方气体方程三维系统的一个特殊子类解。这些解的性质完全由常微分方程的高阶非线性系统表征。与相应的二维模型不同，该系统的所有奇异点都被发现是不稳定的。已经发现了该系统的一些第一积分。在轴对称的情况下，系统可以简化为单个方程。如果绝热指数等于 2，则系统是可积的。