  We study the nonlinear coupling coefficients appearing in the Manakov
equations for multimode fibers (MMF) for space-division multiplexing operating
in the two regimes of strong coupling only within mode groups and strong
coupling also across mode groups. The analysis is mainly focused on the
trenchless parabolic graded-index MMFs, but considerations on the step-index
profile, and on the use of realistic trenches and non-parabolic indices are
given. Analytic results for the Manakov nonlinearity coefficients are derived
for the first time, and validation is performed through a numerical approach.
We show that the coefficients are approximately independent on the fiber core
radius and refractive index difference, but depend only on the number of guided
modes. Values of nonlinear coefficients are computed also for optimized and
manufactured MMFs described in the literature, and are placed within the
developed framework. The impact of a poor fiber design on the achievable data
rates of the MMF nonlinear channel is discussed for a simple scenario.
