  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.
