  We derive coupled propagation equations for ultrashort pulses in a degenerate
three-wave mixing process in quadratic media, using approximations consistent
with the slowly evolving wave approximation [T. Brabec and F. Krausz, Phys.
Rev. Lett. 78, 3282 (1997)]. From these we derive an approximate single-field
equation for the fundamental field. This document expands upon mathematics used
for work submitted by the same authors to Physical Review Letters.
