143 citations · 2.7k across the 108 of their papers we have counts for
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Reduction operators of Burgers equation
Oleksandr A. Pocheketa, Roman O. Popovych
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the sp…
Complete point symmetry group of the barotropic vorticity equation on a rotating sphere
Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych
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 inva…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients
Vyacheslav M. Boyko, Roman O. Popovych, Nataliya M. Shapoval
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The ex…
Singular reduction modules of differential equations
Vaycheslav M. Boyko, Michael Kunzinger, Roman O. Popovych
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation…
Invariant discretization schemes for the shallow-water equations
Alexander Bihlo, Roman O. Popovych
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing…