Derivation of Nonlinear Evolution Equations for Coupled and Single   Fields in a Quadratic Medium
  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. 
Jeffrey Moses and Frank W. Wise