Combination of Born–Infeld and Conformally Invariant Maxwell Lagrangians

Considering the advantages of two independent nonlinear electrodynamic models, we are going to combine them to obtain a unified theory. Taking into account the functional form of both the Born–Infeld and conformally invariant Maxwell Lagrangians, we use the composition method of two arbitrary functions F ( x ) and G ( x ) ( F o G ( x ) = F ( G ( x ) ) and G o F ( x ) = G ( F ( x ) ) ) to obtain a new nonlinear Lagrangian. We obtain an electric field related to this new Lagrangian by solving a nonlinear differential equation. The numerical results are in excellent agreement with the analytical solutions in special limits and we expect that our numerical code precisely predict the behavior of the electric field for more general cases.