Complete point symmetry group of the barotropic vorticity equation on a rotating sphere

摘要

The complete point symmetry group of the barotropic vorticity equation on a rotating 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 point symmetry 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.