2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57108We construct nonlinear representations of the Poincare, Galilei, and conformal algebras on a set of the vector-functions $Ψ=(\vec E, \vec H)$. 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 correctedMathematical PhysicsRepresentation TheoryExactly Solvable and Integrable SystemsQuantum Physics81R05, 20C35, 22E70, 35A30, 58J70, 78A25text