旋转球上正压涡度方程的完全点对称群
Complete point symmetry group of the barotropic vorticity equation on a rotating sphere
摘要：
确定了球面正压涡度方程的完全点对称群。我们使用的方法依赖于由相关组生成的自同构下的微分方程系统的最大李不变性代数的超理想的不变性。一个方便的集的巨理想的最大李不变代数的球涡度方程。我们证明了这个方程只有两个独立的离散对称（直到与连续点对称变换的组合）。
英文摘要：
The complete point symmetry group of the barotropic vorticity equation on the sphere is determined. The method we use relies on the invariance of megaideals of the maximal Lie invariance algebra of a system of differential equations under automorphisms generated by the associated group. A convenient set of megaideals is found for the maximal Lie invariance algebra of the spherical vorticity equation. We prove that there are only two independent (up to composition with continuous point symmetry transformations) discrete symmetries for this equation.
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