2019
Том 71
№ 11

All Issues

Zhdanov R. Z.

Articles: 9
Article (Russian)

On new realizations of the poincare groups P (1,2) and P(2, 2)

Lagno V. I., Zhdanov R. Z.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 4. - pp. 447-462

We classify realizations of the Poincare groups P (1, 2) and P (2, 2) in the class of local Lie groups of transformations and obtain new realizations of the Lie algebras of infinitesimal operators of these groups.

Brief Communications (Russian)

Integrability of Riccati equations and stationary Korteweg-de vries equations

Zhdanov R. Z.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 856–860

By using the Lie infinitesimal method, we establish the correspondence between the integrability of a one-parameter family of Riccati equations and the hierarchy of the higher Korteweg-de Vries equations.

Article (Ukrainian)

Reduction of differential equations and conditional symmetry

Tsifra I. M., Zhdanov R. Z.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 595-602

We determine conditions under which partial differential equations are reducible to equations with a smaller number of independent variables and show that these conditions are necessary and sufficient in the case of a single dependent variable.

Article (English)

Reduction of the self-dual Yang-Mills equations I. Poincaré group

Fushchich V. I., Lagno V. I., Zhdanov R. Z.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 456–462

For the vector potential of the Yang-Mills field, we give a complete description of ansatzes invariant under three-parameterP (1, 3) -inequivalent subgroups of the Poincaré group. By using these ansatzes, we reduce the self-dual Yang-Mills equations to a system of ordinary differential equations.

Article (English)

Separation of variables in two-dimensional wave equations with potential

Fushchich V. I., Revenko I. V., Zhdanov R. Z.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1343–1361

The paper is devoted to solution of a problem of separation of variables in the wave equation $u_{tt} - u_{xx} + V(x)u = 0$. We give a complete classification of potentials $V(x)$ for which this equation admits a nontrivial separation of variables. Furthermore, we obtain all coordinate systems that provide separability of the equation considered.

Article (Ukrainian)

General solutions of the nonlinear wave equation and of the eikonal equation

Fushchich V. I., Revenko I. V., Zhdanov R. Z.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 11. - pp. 1471–1487

Article (Ukrainian)

Symmetry and exact solutions of nonlinear Galilei-invariant equations for a spinor field

Zhdanov R. Z.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 4. - pp. 496-503

Article (Ukrainian)

Some exact solutions of the non-linear Dirac-Hamilton system

Zhdanov R. Z.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 610–616

Article (Ukrainian)

Exact solutions of the nonlinear Dirac equation in terms of Bessel, Gauss and Legendre functions and Chebyshev-Hermite polynomials

Revenko I. V., Zhdanov R. Z.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 4. - pp. 564–568