In this paper group properties of the so-called Generalized Burnett equations are studied. In contrast to the classical Burnett equations these equations are well-posed and therefore can be used in applications. We consider the one-dimensional version of the generalized Burnett equations for Maxwell molecules in both Eulerian and Lagrangian coordinates and perform the complete group analysis of these equations. In particular, this includes finding and analyzing admitted Lie groups. Our classifications of the Lie symmetries of the Navier-Stokes equations of compressible gas and generalized Burnett equations provide a basis for finding invariant solutions of these equations. We also consider representations of all invariant solutions. Some particular classes of invariant solutions are studied in more detail by both analytical and numerical methods.

在本文中，研究了所谓的广义伯内特方程组的性质。与经典的Burnett方程相反，这些方程的位置很好，因此可以在应用中使用。我们考虑在欧拉坐标和拉格朗日坐标中针对麦克斯韦分子的广义伯内特方程的一维形式，并对这些方程进行完整的组分析。特别是，这包括查找和分析被接纳的李群。我们对可压缩气体的Navier-Stokes方程和广义Burnett方程的Lie对称性的分类为寻找这些方程的不变解提供了基础。我们还考虑所有不变解的表示。通过分析和数值方法对某些特定类别的不变解进行了更详细的研究。