Two-dimensional solutions for Born-Infeld fields

TL;DR

This paper presents a method to solve the non-linear Born-Infeld equation by reducing it to a first-order complex equation, enabling explicit solutions for electrostatics, magnetostatics, and wave propagation.

Contribution

It introduces a novel reduction technique transforming the Born-Infeld equation into a solvable complex equation, simplifying analysis of non-linear fields.

Findings

Explicit solutions for electrostatics and magnetostatics

Method applicable to wave propagation problems

Boundary conditions determine unique solutions

Abstract

The non-linear second order Born-Infeld equation is reduced to a simpler first order complex equation, which can be trivially solved for the coordinates as functions of the field. Each solution is determined by the choice of a holomorphic function subjected to boundary conditions. The explanation of the method is accompanied by applications to Born-Infeld electrostatics, magnetostatics and wave propagation.