143 citations · 757 across the 54 of their papers we have counts for
24 papers · 1 filter
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…
Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations
Olena O. Vaneeva, Alexander Bihlo, Roman O. Popovych
Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissibl…
Zeroth-order conservation laws of two-dimensional shallow water equations with variable bottom topography
Alexander Bihlo, Roman O. Popovych
We classify zeroth-order conservation laws of systems from the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the me…
Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations
Stanislav Opanasenko, Alexander Bihlo, Roman O. Popovych
We study admissible transformations and Lie symmetries for a class of variable-coefficient Burgers equations. We combine the advanced methods of splitting into normalized subclasse…
Differential invariants for a class of diffusion equations
Elsa Dos Santos Cardoso-Bihlo, Alexander Bihlo, Roman O. Popovych
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is…
Inverse problem on conservation laws
Roman O. Popovych, Alexander Bihlo
The explicit formulation of the general inverse problem on conservation laws is presented for the first time. In this problem one aims to derive the general form of systems of diff…