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

Elsa Dos Santos Cardoso-Bihlo; Roman O. Popovych

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

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arxiv 1206.6919 v4 pith:QVZ3M2RK submitted 2012-06-29 math-ph math.MPphysics.ao-phphysics.flu-dyn

Elsa Dos Santos Cardoso-Bihlo , Roman O. Popovych This is my paper · ORCID

classification math-phmath.MPphysics.ao-phphysics.flu-dyn

keywords equationgroupinvariancepointsymmetryvorticityalgebrabarotropic

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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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Extended symmetry analysis of two-dimensional degenerate Burgers equation
math.AP 2019-08 accept novelty 7.0 of 10

For the degenerate Burgers equation u_t + u u_x - u_yy = 0, all generalized symmetries reduce to Lie symmetries, and conservation laws are in one-to-one correspondence with solutions of the backward heat equation.

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