Standing wave solutions in Born-Infeld theory

TL;DR

This paper investigates standing wave solutions in Born-Infeld electrodynamics between parallel plates, employing iterative and minimal surface methods, and explores effects of a uniform magnetic background.

Contribution

It introduces two novel methods for finding standing wave solutions in Born-Infeld theory and analyzes their behavior under different electromagnetic backgrounds.

Findings

Successful application of iterative and minimal surface methods

Existence of standing wave solutions in various magnetic backgrounds

Insights into nonlinear scalar Born-Infeld equation solutions

Abstract

We study standing-wave solutions of Born-Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the electromagnetic field has only one nonzero component depending on time and on the coordinate perpendicular to the plates. The problem then reduces to solving the scalar Born-Infeld equation, a nonlinear partial differential equation in 1+1 dimensions. We apply two alternative methods to obtain standing-wave solutions to the Born-Infeld equation: an iterative method, and a ``minimal surface'' method. We also study standing wave solutions in a uniform constant magnetic field background.