Lie reduction and exact solutions of vorticity equation on rotating sphere

摘要

Following our paper [J. Math. Phys. 50 (2009) 123102], we systematicallycarry out Lie symmetry analysis for the barotropic vorticity equation on therotating sphere. All finite-dimensional subalgebras of the correspondingmaximal Lie invariance algebra, which is infinite-dimensional, are classified.Appropriate subalgebras are then used to exhaustively determine Lie reductionsof the equation under consideration. The relevance of the constructed exactsolutions for the description of real-world physical processes is discussed. Itis shown that the results of the above paper are directly related to theresults of the recent letter by N. H. Ibragimov and R. N. Ibragimov [Phys.Lett. A 375 (2011) 3858] in which Lie symmetries and some exact solutions ofthe nonlinear Euler equations for an atmospheric layer in spherical geometrywere determined.