  A Gaussian noise (GN) model is presented that properly accounts for an
arbitrary frequency dependent signal power profile along the link. This enables
the evaluation of the impact of inter-channel stimulated Raman scattering
(ISRS) on the optical Kerr nonlinearity. Additionally, the frequency dependent
fiber attenuation can be taken into account and transmission systems that use
hybrid amplification schemes can be modeled, where distributed Raman
amplification is partly applied over the optical spectrum. To include the
latter two cases, a set of coupled ordinary differential equations must be
numerically solved in order to obtain the signal power profile yielding a
semi-analytical model. However for lumped amplification and negligible
variation in fiber attenuation, a less complex and fully analytical model is
presented which is referred to as the ISRS GN model. The derived model is exact
to first-order for Gaussian modulated signals and extensively validated by
numerical split-step simulations. A maximum deviation of $0.1$~dB in nonlinear
interference power between simulations and the ISRS GN model is found. The
model is applied to a transmission system that occupies an optical bandwidth of
$10$~THz, representing the entire C+L band. At optimum launch power, changes of
up to $2$~dB in nonlinear interference power due to ISRS are reported.
Furthermore, comparable models published in the literature are benchmarked
against the ISRS GN model.
