2019
Том 71
№ 6

All Issues

Popovich R. O.

Articles: 6
Article (English)

Sharpening of the Explicit Lower Bounds for the Order of Elements in Finite Field Extensions Based on Cyclotomic Polynomials

Popovich R. O.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Group Classification of Generalized Eikonal Equations

Egorchenko I. A., Popovich R. O.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Group Classification of Nonlinear Schrödinger Equations

Nikitin A. G., Popovich R. O.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

On Navier-Stokes fields with linear vorticity

Popovich G. V., Popovich R. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1223–1229

We describe all Navier-Stokes fields with vorticity linear in space variables.

Article (Ukrainian)

On the navier-stokes equation with the additional condition $u_1^1 = u^3 = 0$

Popovich R. O., Popovich V. O.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

On the symmetry and exact solutions of a certain transport equation

Popovich R. O.

↓ Abstract   |   Full text (.pdf)

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.