Iryna Yehorchenko

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematical Physics, Applied Mathematics, Geometry and Topology, Modeling and Simulation

Scopus Publications

Differential Invariants, Hidden and Conditional Symmetry
I. A. Yehorchenko
Springer Science and Business Media LLC



Solutions of the system of d'Alembert and eikonal equations, and classification of reductions of PDEs
Irina Yehorchenko
IOP Publishing
We present an approach to systematic description and classification of solutions of partial differential equations that are obtained by means of reduction of these equations to other equations with smaller number of independent variables. We propose to classify such reductions by means of classification of reduction conditions. The approach is illustrated by an example of the system of d'Alembert and eikonal equations. Solutions of this system were used to outline classification of reductions for the general nonlinear d'Alembert equation, with generalisation to arbitrary Poincaré invariant equations.


Group classification of generalized eikonal equations
R. O. Popovych and I. A. Ehorchenko
Springer Science and Business Media LLC



Second-order differential invariants for some extensions of the poincaré group and invariant equations
V.F. Kovalev, S.V. Krivenko, and V.V. Pustovalov
Springer Science and Business Media LLC



Second-order differential invariants of the rotation group O(n) and of its extensions: E(n), P(1, n), G(1, n)
W. I. Fushchich and I. A. Yegorchenko
Springer Science and Business Media LLC



Non-Lie ansatzen and conditional symmetry of the nonlinear Schrödinger equation
V. I. Fushchich and I. A. Egorchenko
Springer Science and Business Media LLC



On the reduction of the nonlinear multi-dimensional wave equations and compatibility of the d'Alembert-Hamilton system
W.I. Fushchich, R.Z. Zhdanov, and I.A. Yegorchenko
Elsevier BV



Differential invariants of a Euclidean algebra
I. A. Egorchenko
Springer Science and Business Media LLC



The symmetry and exact solutions of the nonlinear d'Alembert equation for complex fields
W I Fushchich and I A Yegorchenko
IOP Publishing
The nonlinear wave equations for the complex scalar field invariant under a conformal group are constructed and multiparametrical exact solutions of certain nonlinear complex d'Alembert equations are found.

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