\documentclass[preview]{standalone}
\usepackage{siunitx}
\usepackage{tikz}
\usepackage[siunitx]{circuitikz}
\usepackage{babel}
\usepackage{acronym}
\newcommand{\At}{A(z, t)}
\newcommand{\Et}{E(z, t)}
\newcommand{\Ew}{\tilde{E}(z, \omega)}
\newcommand{\PNL}{\tilde{\mathrm{P}}^\mathrm{NL}}

\begin{document}
Complex envelope such that $|A|^2$ is in W with E in V/m~:
\begin{equation}
    \At = \sqrt{\frac12 \epsilon_0 c n A_\mathrm{eff}} \Et
\end{equation}

Equations with E in V/m
\begin{equation}
    \frac{\partial \Ew}{\partial z} = i\left(\beta(\omega) - \frac{\omega}{\nu} \right)\Ew + i \frac{\omega^2}{2c\epsilon_0 \beta(\omega)}\PNL(z, \omega)
\end{equation}

\begin{equation}
    \tau = t - \frac{z}{\nu}
    \,, \quad \xi = z
    \,, \quad \frac{\partial}{\partial z} = -\frac1{\nu}\frac{\partial}{\partial \tau} + \frac{\partial}{\partial \xi} = -\frac{i \omega}{\nu} + \frac{\partial}{\partial \xi}
    \,, \quad \frac{\partial}{\partial t} = \frac{\partial}{\partial \tau}
\end{equation}
$\Rightarrow$
\begin{equation}
    \frac{\partial \Ew}{\partial z} = i\beta(\omega)\Ew + i \frac{\omega^2}{2c\epsilon_0 \beta(\omega)}\PNL(z, \omega)
\end{equation}

\end{document}