**Definition 0.0.1 **  The **slowly varying amplitude approximation** assumes that the fractional change of the amplitude of one of the waves in a nonlinear process on the distance of the wavelength $\lambda$ is small.$\newcommand\abs[1]{\left|#1\right|}$
\[\abs{\frac{\partial^2 E}{dz^2}} << \abs{k\frac{\partial E}{\partial z}}\]