143 citations · 2.7k across the 108 of their papers we have counts for
110 papers
Lie and point symmetries of Nyzhnyk models
Oleksandra O. Vinnichenko, Vyacheslav M. Boyko, Roman O. Popovych
We consider a hierarchy of models that can be obtained from the original Nyzhnyk system by imposing conditions on parameters, introducing potentials or pseudopotentials, performing…
Symmetry analysis and exact solutions of multi-layer quasi-geostrophic problem
Serhii D. Koval, Alex Bihlo, Roman O. Popovych
We carry out an extended symmetry analysis of the multi-layer quasi-geostrophic problem. This model is given by a system of an arbitrary number of coupled barotropic vorticity equa…
Hidden symmetries, hidden conservation laws and exact solutions of dispersionless Nyzhnyk equation
Oleksandra O. Vinnichenko, Vyacheslav M. Boyko, Roman O. Popovych
Among Lie submodels of the (real symmetric potential) dispersionless Nyzhnyk equation, we single out a remarkable submodel as such that, despite being the only one, is associated w…
On the prolongation of a local hydrodynamic-type Hamiltonian operator to a nonlocal one
Stanislav Opanasenko, Roman O. Popovych
Nonlocal Hamiltonian operators of Ferapontov type are well-known objects that naturally arise local from Hamiltonian operators of Dubrovin-Novikov type with the help of three const…
Generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation
Dmytro R. Popovych, Serhii D. Koval, Roman O. Popovych
Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov…
Algebraic method of group classification for semi-normalized classes of differential equations
Celestin Kurujyibwami, Dmytro R. Popovych, Roman O. Popovych
We generalize the notion of semi-normalized classes of systems of differential equations, study properties of such classes and extend the algebraic method of group classification t…