18 citations · 39 across the 8 of their papers we have counts for
8 papers
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…
Generic graded contractions of Lie algebras
Mikhail V. Kochetov, Serhii D. Koval
We study generic graded contractions of Lie algebras from the perspectives of group cohomology, affine algebraic geometry and monoidal categories. We show that generic graded contr…
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…
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…
Subalgebras of Lie algebras. Example of sl(3,R) revisited
Yevhenii Yu. Chapovskyi, Serhii D. Koval, Olha Zhur
Revisiting the results by Winternitz [Symmetry in physics, CRM Proc. Lecture Notes 34, American Mathematical Society, Providence, RI, 2004, pp. 215-227], we thoroughly refine his c…
Extended symmetry analysis of (1+2)-dimensional fine Kolmogorov backward equation
Serhii D. Koval, Roman O. Popovych
Within the class of (1+2)-dimensional ultraparabolic linear equations, we distinguish a fine Kolmogorov backward equation with a quadratic diffusivity. Modulo the point equivalence…
Point and generalized symmetries of the heat equation revisited
Serhii D. Koval, Roman O. Popovych
We derive a nice representation for point symmetry transformations of the (1+1)-dimensional linear heat equation and properly interpret them. This allows us to prove that the pseud…
Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation
Serhii D. Koval, Alexander Bihlo, Roman O. Popovych
We carry out the extended symmetry analysis of an ultraparabolic Fokker-Planck equation with three independent variables, which is also called the Kolmogorov equation and is single…