Approximated solutions to Born-Infeld dynamics

TL;DR

This paper develops an explicit perturbative method to find approximate solutions to the Born-Infeld equation, enabling analysis of electromagnetic wave propagation and interface effects with potential experimental implications.

Contribution

It introduces a symmetry-based perturbative approach to explicitly solve the Born-Infeld equation, improving upon implicit solutions and applying it to wave interactions and interface phenomena.

Findings

Explicit approximate solutions for Born-Infeld electromagnetic waves.

Identification of reflected waves at interfaces with magnetostatic fields.

Potential experimental effects in wave propagation phenomena.

Abstract

The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.