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…
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…
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…
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…