  We develop a model for the description of nonlinear pulse propagation in
multimode optical fibers with a parabolic refractive index profile. It consists
in a 1+1D generalized nonlinear Schr\"odinger equation with a periodic
nonlinear coefficient, which can be solved in an extremely fast and efficient
way. The model is able to quantitatively reproduce recently observed phenomena
like geometric parametric instability and broadband dispersive wave emission.
We envisage that our equation will represent a valuable tool for the study of
spatiotemporal nonlinear dynamics in the growing field of multimode fiber
optics.
