理想磁流体动力学方程的约化及其精确解
Reduction and Exact Solutions of the Ideal Magnetohydrodynamic Equations
摘要：
本文利用对称约化方法得到了（3+1）维理想磁流体动力学方程的不变解。这些方程在伽利略相似李代数下是不变的，对于该李代数，已知r维子代数（$1\leq r\leq 4$）的共轭类的分类。因此，我们限制我们的研究，三维伽利略相似子代数，给出系统组成的常微分方程。我们在这里提出这些解决方案的几个例子。其中一些精确解显示出有趣的物理解释。
英文摘要：
In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the classification by conjugacy classes of r-dimensional subalgebras ($1\leq r\leq 4$) was already known. So we restrict our study to the three-dimensional Galilean-similitude subalgebras that give systems composed of ordinary differential equations. We present here several examples of these solutions. Some of these exact solutions show interesting physical interpretations.
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