Averaged nonlinear equations for multimode fibers valid in all regimes of random linear coupling

We develop averaged equations to model nonlinear propagation in multimode fibers that are valid in all regimes of random, linear, intermodal coupling. The propagation equations apply to the three existing regimes of linear coupling - the two previously studied all-mode (strong) and mode-group (weak) couplings and the new intermediate coupling regime. The equations are therefore general and can describe nonlinear propagation for all types of intermodal linear coupling that can exist between modes in a fiber supporting multiple spatial modes. Numerical simulations are performed to validate the new averaged propagation equations in the nonlinear regime.