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

TL;DR

This paper constructs explicit finite-energy solutions to the nonlinear equations of Born-Infeld electrodynamics, demonstrating that finite total charges imply finite total energy and resolving energy divergence issues in dyonic point charges.

Contribution

It provides explicit solutions to Born-Infeld equations for continuous charge distributions, linking finite charges to finite energy and addressing longstanding divergence problems.

Findings

Finite-energy solutions are explicitly constructed.

Finite total charges guarantee finite total energy.

Resolves energy divergence in dyonic point charge cases.

Abstract

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.