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Reduction and Exact Solutions of the Ideal Magnetohydrodynamic Equations

Philippe Picard
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Abstract

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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Philippe Picard. 2006-11-26. Reduction and Exact Solutions of the Ideal Magnetohydrodynamic Equations. https://arxiv.org/abs/math-ph/0509048

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