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The time derivative term inside GNLSE models the dispersion of
the nonlinearity. This is usually associated with effects such as self-steepening and optical shock formation, characterized by a timescale \tau_0 = 1/\omega_0. In the context of fibre propagation, an additional dispersion of the nonlinearity arises due to the frequency dependence of the effective mode area. The last effect can be accounted in \tau_0 coefficient in an approximate manner.
A better - still approximate - approach to include the dispersion of the effective mode area is to describe it directly in the frequency domain [J07]_. In this case, we can derive a GNLSE for the pulse evolution using \gamma(\omega) defined as
\overline{\gamma}(\omega) =
\frac{n_2n_{\mathrm{eff}}(\omega_0)\omega_0}
{\mathrm{c}n_\mathrm{eff}(\omega)\sqrt{A_{\mathrm{eff}}(\omega)A_{\mathrm{eff}}(\omega_0)}}.
This approach is more rigorous than the approximation of (\gamma = \gamma(\omega_0)) and requires the definition of a pseudo-envelope C(z, \omega) as
C(z, \omega) = \frac{A_{eff}^{1/4}(\omega_0 )}{A_{eff}^{1/4}(\omega )} A(z, \omega).
.. autoclass:: gnlse.NonlinearityFromEffectiveArea