Point symmetry group of the barotropic vorticity equation

The complete point symmetry group of the barotropic vorticity equation on the $\beta$-plane is computed using the direct method supplemented with two different techniques. The first technique is based on the preservation of any megaideal of the maximal Lie invariance algebra of a differential equation by the push-forwards of point symmetries of the same equation. The second technique involves a priori knowledge on normalization properties of a class of differential equations containing the equation under consideration. Both of these techniques are briefly outlined.

💡 Research Summary

The paper addresses the complete point symmetry group of the barotropic vorticity equation (BVE) on the β‑plane, a fundamental model in geophysical fluid dynamics that captures the evolution of large‑scale atmospheric and oceanic flows under the latitudinal variation of the Coriolis parameter. While the maximal Lie invariance algebra (the continuous symmetry algebra) of the BVE is well known, the authors emphasize that a full understanding of the equation’s symmetry structure requires the determination of its entire point symmetry group, which includes both continuous and discrete transformations.

The authors begin by writing the BVE in the standard form
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