143 citations · 2.7k across the 108 of their papers we have counts for
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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…
Surprising symmetry properties and exact solutions of Kolmogorov backward equations with power diffusivity
Serhii D. Koval, Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych
Using the original advanced version of the direct method, we efficiently compute the equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov backward equ…
Generalized symmetries of Burgers equation
Dmytro R. Popovych, Alex Bihlo, Roman O. Popovych
Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap…