Symmetry Analysis of Barotropic Potential Vorticity Equation |
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Authors: | Alexander Bihlo and Roman O Popovych |
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Institution: | 1.Faculty of Mathematics, University of Vienna, Nordbergstraβe 15,;A-1090 Vienna, Austria
;2.Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Str.,;01601.Kyiv, Ukraine |
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Abstract: | Recently F. Huang Commun. Theor. Phys. 42 (2004) 903] and X. Tang and P.K. Shukla Commun. Theor. Phys. 49 (2008) 229] investigated symmetry properties of the barotropic potential vorticity equation without forcing anddissipation on the beta-plane. This equation is governed by two dimensionless parameters, F and β, representing the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth' angular rotation, respectively. In the present paper it is shown that in the case F≠ 0 there exists a well-defined point transformation to set β= 0. Theclassification of one- and two-dimensional Lie subalgebras of the Lie symmetry algebra of the potential vorticity equation is given for the parameter combination F≠0 and β = 0. Based upon this classification, distinct classes of group-invariant solutions are obtained and extended to the case β≠ 0. |
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Keywords: | potential vorticity equation Lie symmetries classification of subalgebras exact solutions |
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