  The equations describing planar magnetoacoustic waves of permanent form in a
cold plasma are rewritten so as to highlight the presence of a naturally small
parameter equal to the ratio of the electron and ion masses. If the magnetic
field is not nearly perpendicular to the direction of wave propagation, this
allows us to use a multiple-scale expansion to demonstrate the existence and
nature of nonlinear wave solutions. Such solutions are found to have a rapid
oscillation of constant amplitude superimposed on the underlying large-scale
variation. The approximate equations for the large-scale variation are obtained
by making an adiabatic approximation and in one limit, new explicit solitary
pulse solutions are found. In the case of a perpendicular magnetic field,
conditions for the existence of solitary pulses are derived. Our results are
consistent with earlier studies which were restricted to waves having a
velocity close to that of long-wavelength linear magnetoacoustic waves.
