论文标题
Lagrangian坐标中一维浅水磁水动力学方程的对称和保护法
Symmetries and conservation laws of the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
论文作者
论文摘要
研究了吉尔曼近似中的一维浅水磁流失动力学方程（SMHD）的对称性。在拉格朗日和欧拉坐标中，在平面和底部不均匀的情况下，考虑了SMHD方程。对称分类将所有底部的地形分开，这些底层形状产生了完全不同的接收对称性。 Lagrangian坐标中的SMHD方程还原为单个二阶PDE。 Lagrangian形式主义和Noether定理用于构建SMHD方程的保护法。获得了一些针对各种底层地形的新保护法。结果也表示在Eulerian坐标中。构建了不变和部分不变的解决方案。
Symmetries of the one-dimensional shallow water magnetohydrodynamics equations (SMHD) in Gilman's approximation are studied. The SMHD equations are considered in case of a plane and uneven bottom topography in Lagrangian and Eulerian coordinates. Symmetry classification separates out all bottom topographies which yields substantially different admitted symmetries. The SMHD equations in Lagrangian coordinates were reduced to a single second order PDE. The Lagrangian formalism and Noether's theorem are used to construct conservation laws of the SMHD equations. Some new conservation laws for various bottom topographies are obtained. The results are also represented in Eulerian coordinates. Invariant and partially invariant solutions are constructed.
