Solution of the equations system of nonlinear electrodynamics minimally coupled to gravity in the axisymmetric case

The main features of electromagnetic fields follow from the analysis of regular solutions of the system of equations of nonlinear electrodynamic minimally coupled to gravity (NED-GR). In this paper, a representation for the derivative of the Lagrangian with respect to the field invariant, which ensures the consistency of the system of equations NED-GR, is found and the exact solution of this system of equations is obtained. Expressions for the components of the electromagnetic field are given.