Cylindrically symmetric self-sustaining solutions in some models of nonlinear electrodynamics

Abstract

In this article, we discuss the extension of the Melvin solution for the geon to some models of non-linear electrodynamics with the exact form of the Lagrangian, in particular, for a conformally invariant model (CNED), whose Lagrangian depends on the second and fourth order invariants of the electromagnetic field tensor.