非线性不可压缩霍尔磁流体方程组的精确解

得到了不可压缩理想霍尔磁流体方程组的平面波精确解，这些平面波是斜传播的左旋圆极化波或右旋圆极化波，并且涨落速度和涨落磁场通过波数联系起来。讨论了这些平面波解的叠加性质。当波的传播方向平行时，任意两支圆极化平面波都可以叠加；而当波的传播方向不平行时，只有极化方向相同，波数相同，且各自的旋度与自身都是同方向(或都是反方向)的两支圆极化平面波才可以叠加。

Exact solutions of the nonlinear incompressible Hall MHD equations

It was showed that the incompressible ideal Hall MHD equations submitted themselves to the plane-wave exact solutions. They were obliquely propagating left-handed or right-handed circular polarized waves. The fluctuating velocity and magnetic field were connected through the wave-number. In addition, the superposition properties of the plane-wave solutions were discussed. It was found that two arbitrary circular polarized plane waves could superpose when their propagating directions were parallel. But when the propagating directions of two circular polarized plane waves were non-parallel, they could superpose only if they had the same polarized direction, the same wave-number, and the curl of each wave and itself were all in the same direction (or opposite direction).