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