Popovich R. O.
Sharpening of the Explicit Lower Bounds for the Order of Elements in Finite Field Extensions Based on Cyclotomic Polynomials
Ukr. Mat. Zh. - 2014. - 66, № 6. - pp. 815–825
We explicitly construct elements of high multiplicative order in any extensions of finite fields based on cyclotomic polynomials.
Ukr. Mat. Zh. - 2001. - 53, № 11. - pp. 1513-1520
By using a new approach to a group classification, we perform a symmetry analysis of equations of the form u a u a = F(t, u, u t) that generalize the well-known eikonal and Hamilton–Jacobi equations.
Ukr. Mat. Zh. - 2001. - 53, № 8. - pp. 1053-1060
We propose an approach to problems of group classification. By using this approach, we perform a complete group classification of nonlinear Schrödinger equations of the form iψ t + Δψ + F(ψ, ψ*) = 0.
Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1223–1229
We describe all Navier-Stokes fields with vorticity linear in space variables.
Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1363-1374
We study the Navier-Stokes equation with the additional condition $u_1^1 = u^3 = 0$. In certain cases, solutions are represented in a closed form. In other cases, the investigated system reduces to simpler systems of partial differential equations. We study the symmetry properties of these systems and construct classes of their particular solutions.
Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 121–125
Both the Lie andQ-conditional symmetry of a certain linear transport equation are studied and classes of its exact solutions are obtained.