Exact Solutions to the Nonlinear Governing Equations of the Born-Infeld Theory

Exact finite-energy solutions to the nonlinear governing equations of the Born-Infeld theory of electrodynamics, describing continuous distributions of electric, magnetic, and dyonic charge sources, in both classical and generalized settings, are constructed explicitly. In particular, it is shown that, the finiteness of the total prescribed charges leads to the finiteness of the total energy, of the electromagnetic field system. As a by-product, this result resolves a puzzle arising in the dyonic point charge distribution situation where energy divergence inevitably occurs.