142 citations · 338 across the 22 of their papers we have counts for
23 papers
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…
Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation
Vyacheslav M. Boyko, Roman O. Popovych, Oleksandra O. Vinnichenko
Applying an original megaideal-based version of the algebraic method, we compute the point-symmetry pseudogroup of the dispersionless (potential symmetric) Nizhnik equation. This i…
Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations
Vyacheslav M. Boyko, Oleksandra V. Lokaziuk, Roman O. Popovych
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables u…
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…