143 citations · 2.7k across the 108 of their papers we have counts for
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More common errors in finding exact solutions of nonlinear differential equations. I
Roman O. Popovych, Olena O. Vaneeva
In the recent paper by Kudryashov [Commun. Nonlinear Sci. Numer. Simulat., 2009, V.14, 3507-3529] seven common errors in finding exact solutions of nonlinear differential equations…
Reduction operators of variable coefficient semilinear diffusion equations with a power source
O. O. Vaneeva, R. O. Popovych, C. Sophocleous
Reduction operators (called often nonclassical symmetries) of variable coefficient semilinear reaction-diffusion equations with power nonlinearity ($m…
Invariants of Lie algebras via moving frames
Vyacheslav Boyko, Jiri Patera, Roman Popovych
A purely algebraic algorithm for computation of invariants (generalized Casimir operators) of Lie algebras by means of moving frames is discussed. Results on the application of the…
Is a nonclassical symmetry a symmetry?
Michael Kunzinger, Roman O. Popovych
Various versions of the definition of nonclassical symmetries existing in the literature are analyzed. Comparing properties of Lie and nonclassical symmetries leads to the conclusi…
Lie symmetries and exact solutions of the barotropic vorticity equation
Alexander Bihlo, Roman O. Popovych
Lie group methods are used for the study of various issues related to symmetries and exact solutions of the barotropic vorticity equation. The Lie symmetries of the barotropic vort…