Nonlinear representations for Poincare and Galilei algebras and   nonlinear equations for electromagnetic fields
  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. 
Wilhelm I. Fushchych, Ivan M. Tsyfra and Vyacheslav M. Boyko