Alexander Bihlo, Roman O. Popovych
Following our paper [J. Math. Phys. 50 (2009) 123102], we systematically
carry out Lie symmetry analysis for the barotropic vorticity equation on the
rotating sphere. All finite-dimensional subalgebras of the corresponding
maximal Lie invariance algebra, which is infinite-dimensional, are classified.
Appropriate subalgebras are then used to exhaustively determine Lie reductions
of the equation under consideration. The relevance of the constructed exact
solutions for the description of real-world physical processes is discussed. It
is shown that the results of the above paper are directly related to the
results 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 of
the nonlinear Euler equations for an atmospheric layer in spherical geometry
were determined.
View original:
http://arxiv.org/abs/1112.3019
No comments:
Post a Comment