  We present a comprehensive framework for treating the nonlinear interaction
of few-cycle pulses using an envelope description that goes beyond the
traditional SVEA method. This is applied to a range of simulations that
demonstrate how the effect of a $\chi^{(2)}$ nonlinearity differs between the
many-cycle and few-cycle cases. Our approach, which includes diffraction,
dispersion, multiple fields, and a wide range of nonlinearities, builds upon
the work of Brabec and Krausz[1] and Porras[2]. No approximations are made
until the final stage when a particular problem is considered.
  The original version (v1) of this arXiv paper is close to the published
Phys.Rev.A. version, and much smaller in size.
