Lagno V. I.
Group classification of quasilinear elliptic-type equations. II. Invariance under solvable Lie algebras
Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 200-215
The problem of the group classification of quasilinear elliptic-type equations in a two-dimensional space is considered. The list of all equations of this type, which admit the solvable Lie algebras of symmetry operators, is obtained. The results of this paper along with results obtained by the authors earlier give a complete solution of the problem of the group classification of quasilinear elliptic-type equations.
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.
Ukr. Mat. Zh. - 1998. - 50, № 3. - pp. 414-423
We study Galilei groups represented as groups of Lie transformations in the space of two independent variables and one dependent variable. We classify the representations of the groups A G 1(1,1), A G 2(1,1), A G 3(1,1), A ~G 1 (1,1), A ~G 2 (1,1), and A ~G3(1,1) in the class of Lie vector fields.
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.
Ukr. Mat. Zh. - 1989. - 41, № 9. - pp. 1169–1172
Subalgebras of the poincare algebra AP (2, 3) and the symmetric reduction of the nonlinear ultrahyperbolic d'Alembert equation. I
Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 411-416