[en] Waves in electron-positron plasmas have fundamentally different dispersion characteristics due to the equal charge-to-mass ratios between negative and positive charges, which mix different timescales, and are of interest in understanding aspects of pulsars and active galactic nuclei, where astrophysical electron-positron plasmas occur. Earlier systematic nonlinear treatments of parallel propagating electromagnetic waves via a reductive perturbation analysis had indicated unusual results, namely a vector equivalent of the modified Korteweg-de Vries equation. The latter is nonintegrable except in the case of linear polarization when it becomes equivalent to the scalar (integrable) modified Korteweg-de Vries equation. Here large amplitude purely stationary nonlinear solitary waves are studied in their own reference frame via the McKenzie approach. The behavior of the wave magnetic field can be expressed through an energy integral that involves the Mach number of the structure. Possible solitons are super-Alfvenic and occur symmetrically for positive or negative fields, owing to the obvious symmetry between positive and negative charges with the same mass. The limits on the allowable Mach numbers and soliton amplitudes have also been computed. (C) 2004 American Institute of Physics.