Department of Mathematical Physics
Institute of Mathematics of the National Academy of Sciences of Ukraine
Mathematical Physics, Applied Mathematics, Geometry and Topology, Modeling and Simulation
I. A. Yehorchenko Springer Science and Business Media LLC
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.
R. O. Popovych and I. A. Ehorchenko Springer Science and Business Media LLC
V.F. Kovalev, S.V. Krivenko, and V.V. Pustovalov Springer Science and Business Media LLC
W. I. Fushchich and I. A. Yegorchenko Springer Science and Business Media LLC
V. I. Fushchich and I. A. Egorchenko Springer Science and Business Media LLC
W.I. Fushchich, R.Z. Zhdanov, and I.A. Yegorchenko Elsevier BV
I. A. Egorchenko Springer Science and Business Media LLC
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.