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Publications Influence

Realizations of real low-dimensional Lie algebras

- R. Popovych, V. M. Boyko, M. Nesterenko, Maxim W. Lutfullin
- Mathematics, Physics
- 21 January 2003

Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a… Expand

144 11- PDF

Admissible Transformations and Normalized Classes of Nonlinear Schrödinger Equations

- R. Popovych, M. Kunzinger, H. Eshraghi
- Mathematics, Physics
- 23 November 2006

The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of… Expand

109 8- PDF

New results on group classification of nonlinear diffusion–convection equations

- R. Popovych, N. M. Ivanova
- Mathematics, Physics
- 12 June 2003

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient (1 + 1)-dimensional nonlinear… Expand

133 4- PDF

Point symmetry group of the barotropic vorticity equation

- Alexander Bihlo, R. Popovych
- Physics, Mathematics
- 8 September 2010

The complete point symmetry group of the barotropic vorticity equation on the $\beta$-plane is computed using the direct method supplemented with two different techniques. The first technique is… Expand

18 3- PDF

Singular reduction operators in two dimensions

- M. Kunzinger, R. Popovych
- Mathematics, Physics
- 26 August 2008

The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All… Expand

23 3- PDF

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

- O. Vaneeva, R. Popovych, C. Sophocleous
- Mathematics, Physics
- 26 August 2007

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between… Expand

86 2- PDF

Exact solutions of a remarkable fin equation

- R. Popovych, C. Sophocleous, O. Vaneeva
- Mathematics, Physics
- Appl. Math. Lett.
- 9 October 2006

TLDR

30 2- PDF

Algebraic method for finding equivalence groups

- Alexander Bihlo, Elsa Dos Santos Cardoso-Bihlo, R. Popovych
- Mathematics, Physics
- 22 March 2015

The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The… Expand

11 2- PDF

Group analysis of nonlinear fin equations

- O. Vaneeva, A. G. Johnpillai, R. Popovych, C. Sophocleous
- Computer Science, Physics
- Appl. Math. Lett.
- 3 October 2006

TLDR

29 2- PDF

Complete point symmetry group of vorticity equation on rotating sphere

- Elsa Dos Santos Cardoso-Bihlo, R. Popovych
- Mathematics
- 29 June 2012

The complete point symmetry group of the barotropic vorticity equation on the sphere is determined. The method we use relies on the invariance of megaideals of the maximal Lie invariance algebra of a… Expand

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