  The vacuum is expected to exhibit electromagnetic nonlinearity. We
demonstrate the properties of nonlinear electromagnetic wave in a
two-dimensional rectangular cavity by calculating the nonlinear correction for
two classical standing waves. We apply the linear approximation in a short
timescale. A part of the nonlinear correction increases with time. In
particular, a one-dimensional second harmonic grows if the cavity size
satisfies a specific condition. We also analyze the nonlinear electromagnetic
wave in a timescale longer than the applicable limit of the linear
approximation. We formulate the self-modulation of the amplitude and phase,
including the effect of static magnetic flux density. In the viewpoint of
energy flow between the two modes of the standing wave, the behavior of
nonlinear electromagnetic wave can be classified into three types. Namely, the
energy flow keeps oscillating, eventually decreases to zero, or never occurs.
