Nonlinear representations for Poincare and Galilei algebras and nonlinear equations for electromagnetic fields

Abstract

We construct nonlinear representations of the Poincare, Galilei, and conformal algebras on a set of the vector-functions $\Psi =(\vec{E},\vec{H})$. A nonlinear complex equation of Euler type for the electromagnetic field is proposed. The invariance algebra of this equation is found.

LaTeX, 10 pages, some misprints of published version corrected