26 citations · 103 across the 9 of their papers we have counts for
9 papers
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…
Mapping method of group classification
Stanislav Opanasenko, Roman O. Popovych
We revisit the entire framework of group classification of differential equations. After introducing the notion of weakly similar classes of differential equations, we develop the…
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…
Equivalence groupoid of a class of general Burgers-Korteweg-de Vries equations with space-dependent coefficients
Stanislav Opanasenko
We describe the equivalence groupoid of the class of general Burgers - Korteweg - de Vries equations with space-dependent coefficients. This class is shown to reduce by a family of…
Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model
Stanislav Opanasenko, Alexander Bihlo, Roman O. Popovych +1
We study the hydrodynamic-type system of differential equations modeling isothermal no-slip drift flux. Using the facts that the system is partially coupled and its subsystem reduc…
Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation
Stanislav Opanasenko, Roman O. Popovych
Using advantages of nonstandard computational techniques based on the light-cone variables, we explicitly find the algebra of generalized symmetries of the (1+1)-dimensional Klein-…
Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusion
Stanislav Opanasenko, Vyacheslav Boyko, Roman O. Popovych
We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version…
Extended symmetry analysis of isothermal no-slip drift flux model
Stanislav Opanasenko, Alexander Bihlo, Roman O. Popovych +1
We perform extended group analysis for a system of differential equations modeling an isothermal no-slip drift flux. The maximal Lie invariance algebra of this system is proved to…
Group analysis of general Burgers-Korteweg-de Vries equations
Stanislav Opanasenko, Alexander Bihlo, Roman O. Popovych
The complete group classification problem for the class of (1+1)-dimensional th order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary va…