2019
Том 71
№ 11

# Zhdanov R. Z.

Articles: 9
Article (Russian)

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

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

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

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

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

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

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

Article (Ukrainian)

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

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

Article (Ukrainian)

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

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

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