Maxwell equations for generalised Lagrangian functional

The author deals with the problem of the construction of the Lagrange functional for an electromagnetic field. The generalised Maxwell equations for an electromagnetic field in free space are introduced. The main idea relies on the change of Lagrange function under the action integral. Usually, the Lagrange functional which describes the electromagnetic field is built with the quadrate of the electromagnetic field tensor F^ik. Such a quadrate term is the reason, from a mathematical point of view, for the linear form of the Maxwell equations in free space. The author does not make this assumption and nonlinear Maxwell equations are obtained. New material parameters of free space are established. The Maxwell equations obtained are quite similar to the well-known Maxwell equations.