  The continuously increasing IP data traffic demand, with geometrical growth
rate exceeding 26%, requires a large transmission capacity increment from the
fiber optical infrastructure. As the deploy of new fiber cables requires
extensive investments, the development of multi-band amplifiers and
transceivers, already available as prototypes, is progressively considered
towards the entire low-loss single-mode bandwidth beyond the 5 THz C-band. In
this perspective, an adequate handling of the variations along the frequency of
the fiber physical features becomes crucial for the fiber propagation modeling
in multi-band wavelength division multiplexing (WDM) channel comb transmission
scenarios. In particular, the inter-channel stimulated Raman scattering (SRS)
is the fundamental inter-band effect in this context. The SRS effect on the WDM
comb propagated through a single-mode optical fiber is described by a set of
ordinary differential equations (ODEs). To date, an exact solution of the SRS
ODEs has not been proposed, and in the literature numerical solutions or
approximations have been considered in order to take into account this effect.
In this work, a perturbative solution of the SRS ODEs is presented enabling an
efficient trade-off between the target accuracy and the computational time.
Considering a C+L+S transmission scenario, the perturbative expansion up to the
2nd order ensures an excellent accuracy. Whereas, in an U-to-E transmission
scenario, the 3rd order is required in order to reach an equivalent accuracy.
