142 citations · 338 across the 22 of their papers we have counts for
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Lie and point symmetries of Nyzhnyk models
Oleksandra O. Vinnichenko, Vyacheslav M. Boyko, Roman O. Popovych
We consider a hierarchy of models that can be obtained from the original Nyzhnyk system by imposing conditions on parameters, introducing potentials or pseudopotentials, performing…
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…
Lie reductions and exact solutions of dispersionless Nizhnik equation
Oleksandra O. Vinnichenko, Vyacheslav M. Boyko, Roman O. Popovych
We exhaustively classify the Lie reductions of the real dispersionless Nizhnik equation to partial differential equations in two independent variables and to ordinary differential…
Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations
Vyacheslav M. Boyko, Oleksandra V. Lokaziuk, Roman O. Popovych
Essentially generalizing Lie's results, we prove that the contact equivalence groupoid of a class of (1+1)-dimensional generalized nonlinear Klein-Gordon equations is the first-ord…
Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations
Olena Vaneeva, Vyacheslav Boyko, Alexander Zhalij +1
A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and "nonclassical" symmetry points o…
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…
Simplest potential conservation laws of linear evolution equations
Vyacheslav M. Boyko, Roman O. Popovych
Every simplest potential conservation law of any (1+1)-dimensional linear evolution equation of even order proves induced by a local conservation law of the same equation. This cla…
Extended symmetry analysis of a "nonconservative Fokker-Plank equation"
Vyacheslav Boyko, Nataliya Shapoval
We show that all results of Yasar and Ozer [Comput. Math. Appl. 59 (2010), 3203-3210] on symmetries and conservation laws of a "nonconservative Fokker-Planck equation" can be easil…
Invariants of Lie algebras via moving frames
Vyacheslav Boyko, Jiri Patera, Roman Popovych
A purely algebraic algorithm for computation of invariants (generalized Casimir operators) of Lie algebras by means of moving frames is discussed. Results on the application of the…
Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements
Vyacheslav Boyko, Jiri Patera, Roman O. Popovych
The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustive…
Invariants of triangular Lie algebras with one nilindependent diagonal element
Vyacheslav Boyko, Jiri Patera, Roman O. Popovych
The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are construct…
Invariants of Triangular Lie Algebras
Vyacheslav Boyko, Jiri Patera, Roman Popovych
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invarian…
Computation of Invariants of Lie Algebras by Means of Moving Frames
Vyacheslav Boyko, Jiri Patera, Roman Popovych
A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's method of moving frames and the kn…
Realizations of Real Low-Dimensional Lie Algebras
Roman O. Popovych, Vyacheslav M. Boyko, Maryna O. Nesterenko +1
Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in…
Continuity Equation in Nonlinear Quantum Mechanics and the Galilei Relativity Principle
Wilhelm I. Fushchych, Vyacheslav M. Boyko
Classes of the nonlinear Schrodinger-type equations compatible with the Galilei relativity principle are described. Solutions of these equations satisfy the continuity equation.
Nonlinear representations for Poincare and Galilei algebras and nonlinear equations for electromagnetic fields
Wilhelm I. Fushchych, Ivan M. Tsyfra, Vyacheslav M. Boyko
We construct nonlinear representations of the Poincare, Galilei, and conformal algebras on a set of the vector-functions . A nonlinear complex equation of Euler…
Differential Invariants and Application to Riccati-Type Systems
Roman Popovych, Vyacheslav Boyko
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and…