8 citations · 22 across the 9 of their papers we have counts for
9 papers
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…
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…
Improving physics-informed DeepONets with hard constraints
Rüdiger Brecht, Dmytro R. Popovych, Alex Bihlo +1
Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equation…
Canonical forms for matrices of Saletan contractions
Dmytro R. Popovych
We show that each Saletan (linear) contraction can be realized, up to change of bases of the initial and the target Lie algebras, by a matrix-function that is completely defined by…
Contractions with necessarily unbounded matrices
Dmytro R. Popovych
We prove that for each dimension not less than five there exists a contraction between solvable Lie algebras that can be realized only with matrices whose Euclidean norms necessari…
Lie-orthogonal operators
Dmytro R. Popovych
Basic properties of Lie-orthogonal operators on a finite-dimensional Lie algebra are studied. In particular, the center, the radical and the components of the ascending central ser…
Equivalence of diagonal contractions to generalized IW-contractions with integer exponents
Dmytro R. Popovych, Roman O. Popovych
We present a simple and rigorous proof of the claim by Weimar-Woods [Rev. Math. Phys. 12 (2000) 1505-1529] that any diagonal contraction (e.g., a generalized Inönü-Wigner contracti…
Lowest dimensional example on non-universality of generalized Inönü-Wigner contractions
Dmytro R. Popovych, Roman O. Popovych
We prove that there exists just one pair of complex four-dimensional Lie algebras such that a well-defined contraction among them is not equivalent to a generalized IW-contraction…