5 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…
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 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…
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…