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This paper presents an alternative {\it relativistic nonlinear} approach tothe vacuum case of classical electrodynamics. Our view is based on theunderstanding that the corresponding differential equations should be dynamicalin nature. So, they must represent local energy-momentum balance relations.Formally, the new equations are in terms of appropriately extended Liederivative of $\mathbb{R}^2$-valued differential 2-form along a$\mathbb{R}^2$-valued 2-vector on Minkowski space-time.

A nonlinear relativistic approach to mathematical representation of vacuum electromagnetism based on extended Lie derivative