77 citations · 182 across the 23 of their papers we have counts for
23 papers
On reduction of multi-dimensional non-linear wave equation to two-dimensional equations
W. I. Fushchych, I. A. Yehorchenko
A condition of reduction of multidimensional wave equations to the two-dimensional equation is studied, and the necessary conditions of compatibility and exact solutions of the res…
Symmetries and Exact Solutions of Nonlinear Dirac Equations
Wilhelm Fushchych, Renat Zhdanov
The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretic…
Second-order differential invariants of the rotation group O(n) and of its extensions: E(n), P(1,n), G(1,n)
W. I. Fushchych, Irina Yehorchenko
Functional bases of second-order differential invariants of the Euclid, Poincaré, Galilei, conformal, and projective algebras are constructed. The results obtained allow us to desc…
Continuity Equation in Nonlinear Quantum Mechanics and the Galilei Relativity Principle
Wilhelm I. Fushchych, Vyacheslav M. Boyko
Classes of the nonlinear Schrodinger-type equations compatible with the Galilei relativity principle are described. Solutions of these equations satisfy the continuity equation.
Nonlinear representations for Poincare and Galilei algebras and nonlinear equations for electromagnetic fields
Wilhelm I. Fushchych, Ivan M. Tsyfra, Vyacheslav M. Boyko
We construct nonlinear representations of the Poincare, Galilei, and conformal algebras on a set of the vector-functions . A nonlinear complex equation of Euler…
Symmetry reduction and exact solutions of the Navier-Stokes equations
Wilhelm I. Fushchych, Roman O. Popovych
Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variabl…