143 citations · 2.7k across the 108 of their papers we have counts for
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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…
Lie symmetries of two-dimensional shallow water equations with variable bottom topography
Alexander Bihlo, Nataliia Poltavets, Roman O. Popovych
We carry out the group classification of the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate sp…
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…
Invariant parameterization of geostrophic eddies in the ocean
Alexander Bihlo, Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych
The framework of invariant parameterization is extended to higher-order closure schemes. We also define, for the first time, generalized invariant parameterization schemes, where s…
Extended symmetry analysis of two-dimensional degenerate Burgers equation
Olena O. Vaneeva, Roman O. Popovych, Christodoulos Sophocleous
We carry out the extended symmetry analysis of a two-dimensional degenerate Burgers equation. Its complete point-symmetry group is found using the algebraic method, and all its gen…