Nonlinear electrodynamics with singularities (modernized Born-Infeld electrodynamics)

Born-Infeld nonlinear electrodynamics are considered. Main attention is given to existence of singular point at static field configuration that M.Born and L.Infeld are considered as; a model of electron. It is shown that such singularities are forbidden within the framework of the Born-Infeld model. It is proposed a modernized action that make possible an existence of the singularities. It is obtained main relations in view of the singularities. In initial approximation this model gives the usual linear electrodynamics with point charged particles.