  Nonlinear electromagnetic waves with superluminal phase velocity can
propagate in the winds around isolated pulsars, and around some pulsars in
binary systems. Using a short-wavelength approximation, we find and analyze an
integrable system of equations that govern their evolution in spherical
geometry. A confined mode is identified that stagnates to finite pressure at
large radius and can form a precursor to the termination shock. Using a
simplified criterion, we find this mode is stable for most isolated pulsars,
but may be unstable if the external pressure is high, such as in the pulsar
wind nebulae in starburst galaxies and in W44. Pulsar winds in eccentric binary
systems, such as PSR 1259-63, may go through phases with stable and unstable
electromagnetic precursors, as well as phases in which the density is too high
for these modes to propagate.
